Baroness Thatcher has died following a stroke, her spokesman Lord Bell said.
Lord Bell said: "It is with great sadness that Mark and Carol Thatcher announced that their mother Baroness Thatcher died peacefully following a stroke on Monday morning.
"A further statement will be made later."
Buckingham Palace said: "The Queen is sad to hear the news of the death of Baroness Thatcher and Her Majesty will be sending a private message of sympathy to the family."
In a statement on the Downing Street Twitter feed, Prime Minister David Cameron said: "It was with great sadness that I learned of Lady Thatcher's death. We've lost a great leader, a great prime minister and a great Briton."
Barrow and Furness MP John Woodcock said: “Whether you loved or loathed her and the effect she had on the country, no-one can ignore that Margaret Thatcher was a formidable conviction politician who left an indelible mark on Britain.
“Our thoughts go to her family at this time.”
Lady Thatcher earned a place in the history books as the first woman prime minister when she entered Downing Street in 1979.
Over the next 11 years even her critics admitted that she changed the face of the country.
In recent years her health deteriorated, and she stopped making public appearances.
Lady Thatcher suffered several small strokes in 2002, and received medical advice against accepting any more public speaking engagements.
Her increasingly frail condition when she was seen - especially after the death of husband Denis in 2003 - led to frequent bouts of speculation about her health.
However, MPs and friends who saw her regularly said she remained alert and interested in politics, and she was not known to have deteriorated notably recently.
There have been calls for the ex-premier to receive a state funeral, although she was a divisive figure for many on the Left.
Work and Pensions Secretary Iain Duncan Smith said Baroness Thatcher was "the reason I came into politics".
He said: "Watching her set out to change Britain for the better in 1979 made me believe there was, at last, real purpose and real leadership in politics once again.
"She bestrode the political world like a colossus.
"This is dreadfully sad news and my thoughts and prayers are with her family."
Senior Tory MP David Davis said: "Margaret Thatcher was the greatest of modern British prime ministers, and was central to the huge transformation of the whole world that took place after the fall of the Soviet Union.
"Millions of people in Britain and around the world owe her a debt of gratitude for their freedom and their quality of life, which was made possible by her courageous commitment to the principles of individual freedom and responsibility.
"Her passing is a very sad event and she will be greatly missed."
Liberal Democrat leader Nick Clegg said: "Margaret Thatcher was one of the defining figures in modern British politics.
"Whatever side of the political debate you stand on, no-one can deny that as prime minister she left a unique and lasting imprint on the country she served.
"She may have divided opinion during her time in politics but everyone will be united today in acknowledging the strength of her personality and the radicalism of her politics.
"My thoughts are with her family and friends."
On his Twitter feed, London Mayor Boris Johnson said: "Very sad to hear of death of Baroness Thatcher. Her memory will live long after the world has forgotten the grey suits of today's politics."
UK Independence Party leader Nigel Farage wrote on Twitter: "Very sad to hear of the death of Margaret Thatcher, a great patriotic lady."
Former employment minister Tony McNulty wrote: "Former Conservative Prime Minister Baroness Thatcher has died following a stroke. God bless her and thoughts are with her family. RIP."
Andrew Selous, Tory MP for South West Bedfordshire, wrote: "Very sorry to learn of Lady Thatcher's death."
Lord Sugar became one of the first to express his condolences, writing: "Margaret Thatcher died today. A great lady she changed the face of British politics, created opportunity for anyone to succeed in the UK. RIP."
In a further posting, he added: "Baroness Thatcher in the 80s kick-started the entrepreneurial revolution that allowed chirpy chappies to succeed and not just the elite."
The life and times of Margaret Thatcher
Margaret Thatcher was the woman who, virtually single-handed and in the space of one tumultuous decade, transformed a nation.
In the view of her many admirers, she thrust a strike-infested half-pace Britain back among the front-runners in the commanding peaks of the industrial nations of the world.
Her detractors, many of them just as vociferous, saw her as the personification of an uncaring new political philosophy known by both sides as Thatcherism.
Tireless, fearless, unshakeable and always in command, she was Britain's first woman Prime Minister - and the first leader to win three General Elections in a row.
Mrs Thatcher, who became Baroness Thatcher, resigned as Prime Minister in November 1990 after a year in which her fortunes plummeted.
It was a year in which she faced a series of damaging resignations from the Cabinet, her own political judgments were publicly denounced by her own colleagues, catastrophic by-election humiliations, internal party strife, and a sense in the country that people had had enough of her after 11 years in power.
But history will almost certainly proclaim her as one of the greatest British peacetime leaders.
Her supporters believe she put the drive back into the British people.
And as she transformed the nation - attempting to release the grip of the state on massive industries and public services alike - she strode the earth as one of the most influential, talked-about, listened-to and dominant statesmen of the Western world.
When Argentina invaded the Falklands, she despatched a task force to the South Atlantic which drove the enemy off the islands in an incomparable military operation 8,000 miles from home.
She successfully defied Arthur Scargill's nationwide and year-long miners' strike, which threatened to cripple Britain's entire economic base.
Her triumphant achievement of power in May 1979 signalled the end of the era when trade union leaders trooped in and out of 10, Downing Street, haggling and bargaining with her Labour predecessors.
Instead she stripped the unions of many of their powers with the aim of transferring them to managements and individual consumers.
Within weeks of her arrival in Downing Street, foreign correspondents from all points of the globe - absent for so long from the House of Commons - flocked back to the press gallery. It was a sure sign that the world was sitting up and listening once again to what Britain had to say.
Whether you liked Mrs Thatcher or loathed her - and her Tory predecessor Edward Heath hated her beyond belief - whether you agreed with her or found her policies utterly repugnant, you could not deny her energy and drive.
Even many political foes secretly admired this single-minded woman, who never contemplated defeat and for whom all issues were black and white, not hedged about with grey.
Even - indeed particularly - her most bitter political enemies were forced to praise her crusading clarity of purpose and her determination, in their eyes, to serve "her people".
Veteran left winger Tony Benn frequently held her up as an example of how a great political party should be led, comparing her with what he regarded as Neil Kinnock's fudged leadership of the Labour Party.
Margaret Thatcher towered above all other political figures in Britain and her dominance of the Cabinet was supreme and rarely challenged. She was the equal of statesmen across the world. She elevated Downing Street to something like the status of the White House and the Kremlin, symbols of the then two great superpowers. Nobody talked down to her.
Yet the Iron Lady - a title bestowed upon her by her enemies in Moscow, which, incidentally she relished - was not all stern, steely and strident. She was delightful with children and she could not disguise her glee - "We are a grandmother" - when her grandson Michael was born in Dallas in February, 1989.
She regularly and touchingly admitted that she could not do her job properly without the unfailing and unstinting support of her "marvellous" husband, Denis. He was, she said, the "golden thread" running through her life. His death, in June 2003, some weeks after major heart surgery, was a profound blow to her.
Sir Denis, as he became after she left Downing Street, was constantly at her side, an impeccable consort, protecting her and guiding her in all weathers and in all parts of the world.
He was a wonderful source of encouragement and comfort to her when, as sometimes happened, she returned home in tears after a particularly gruelling day. He made no attempt to disguise his contempt for those who opposed his wife, but he never got involved publicly in policy or political discussions.
His death came at a time when Margaret Thatcher's own health - she was ten years younger than him - was the subject of speculation. She had suffered a series of strokes and her doctors had forbidden her to make any more speeches - instructions which she was occasionally known to breach.
Sir Denis's death was a massive blow to Lady Thatcher. But there was more grim trouble ahead.
Her son, Sir Mark - he inherited the baronetcy from his father - was charged in South Africa in connection with a plot to overthrow the Government of oil-rich Equatorial Guinea. The charge carried a maximum penalty of 15 years, and possible death if Sir Mark was extradited to Equatorial Guinea.
The news broke when Lady Thatcher was on holiday in the United States. She doted on her son and the charge plainly devastated her.
However, after weeks under house arrest in Capetown, where he lived, Mark in January 2005, pleaded guilty to unwittingly helping to finance a foiled coup plot in oil-rich Equatorial Guinea. He accepted a three million rand fine and a suspended jail sentence.
Judge Abe Motala told him to pay the fine as part of the plea deal, but if he failed to do so by January 17 that year, he faced a five-year prison sentence with a further four years suspended for five years.
Meanwhile his wife Diane and their two children had returned to Dallas, and he planned to rejoin them immediately. However his conviction led to problems about his entry into the United States and instead he returned to London to stay with his mother.
For her it was a massive relief that her son avoided a long prison sentence and also, more traumatically, avoided what could have resulted in a fatal extradition to Equatorial Guinea.
Thatcher always conceded, too, that personal attacks on her, and particularly on members of her family, wounded her deeply. And yet the woman who took on Argentina and who had the people of Moscow reaching out and yearning to touch her, could not bear the sight of creepy-crawlies or snakes.
Mrs Thatcher was obsessively British, batting for Britain wherever she went, wearing exquisite home-produced clothes, upbraiding those who did not, and turning up her nose at the French Perrier Water. "What's wrong with British water?" she demanded.
Her dramatic downfall came about during the second of two challenges to her leadership. She realised that if she stayed on to take her challenger Michael Heseltine - a man she disliked intensely, personally and politically - into a second ballot, he would almost certainly supplant her. That was a prospect she could not bear to see happen.
And so, after consulting her Cabinet colleagues, one by one, she decided she must go, and tearfully gave the Cabinet the news the following morning.
By doing so, she paved the way for one of her favourite "sons" John Major to follow her into 10, Downing Street. But her support for him was luke-warm. She was to say later that she backed him because he was "the best of a poor bunch".
She marked her decision to quit with the historic expression: "It's a funny old world" - pointing out that she had been summarily removed from power even though she had won every election she had fought.
Some of her friends believed that her decision to go to Paris, rather than remain in Westminster, during that first fateful ballot, demonstrated an arrogance and a misjudgment which may well have cost her those crucial handful of votes which would have kept her in Downing Street. If she had received just four more votes, there would have been no need for a second ballot.
But there was no let-up in her energetic activities once she arrived in the House of Lords. She remained a ferocious critic of the European Union, and led a crusade in the Upper House against the Maastricht Treaty.
She was accused, as well, of attacking her successor, John Major, in the same way that her predecessor, Sir Edward Heath, had constantly criticised her when she was in power. But her strictures on John Major did not carry the bitterness and resentment of Heath's criticisms of her.
Years later, she was to be praised by two Labour Prime Ministers, Tony Blair and Gordon Brown, both of whom invited her into Downing Street soon after they came to power. These were events which enraged some factions in the Labour Party.
Baroness Thatcher maintained a gruelling programme of lecture tours worldwide, showing little, if any, sign of slowing down her scorching pace. But there were moments when her stamina and health came into question.
Once, in 1994, she collapsed in the middle of a speech in Santiago, Chile. but she shrugged off warnings from her friends that she should start to take things more easily.
And later that year, her friends were shocked at her gaunt and haggard aspect, three days before her 69th birthday, when she made a token appearance on the platform of the Tory Party conference in Bournemouth.
Her response to that renewed expression of alarm among her supporters was to dash off on another exhausting global speaking tour.
But there was little doubt that her health was affected by the combination of a massive four-hour dental operation, an enforced diet, and worry about reports of her son Mark's alleged profiteering from Middle East arms deals she had negotiated as Prime Minister, as well as the apparently impending break-up of his marriage. But those reports came to nothing.
But neither age nor anything else was going to stop this woman from expressing herself vigorously and passionately whenever she felt the need. In 1997, she derided the British Airways decision to introduce "modern art" on the tailfins of their fleet instead of the symbol of the Union Flag.
She famously covered one of these offending tailfins on the model of an aircraft with a handkerchief while touring the stalls at the Tory Party conference.
And in October, 1998 she called for the immediate release of ex-President Pinochet of Chile, who was being held to face an extradition request by Spain for alleged murder.
Baroness Thatcher said he saved many British lives during the Falklands conflict, that Chile was "a good friend to this country" and that Pinochet must be allowed to return to his own country forthwith.
She caused a stir by visiting the former Chilean leader while he was effectively under house arrest near London, and having lunch with him. But her appeals to the then Home Secretary Jack Straw were ignored.
Before that, in a last-minute move, she backed the Tory leadership campaign of William Hague, support which may have helped him to defeat his rivals by an unexpectedly large margin.
Margaret Hilda Roberts was born in 1925 in the Lincolnshire town of Grantham. She quickly had the virtues of thrift, hard work, morality and patriotism drilled into her by her beloved father Alderman Alfred Roberts, who ran two grocers' shops and a post-office, and became mayor of the town in 1943.
Alderman Roberts was a devout Methodist, a lay preacher and a proudly self-made man. Margaret never forgot - and throughout her career never tired of quoting - his words to her: "You'll never get anywhere if you don't work, girl."
Not only that, but she acted on it. For it was her colossal industry, her almost innocent belief that all her objectives not only could but would be achieved which launched her into a political career unsurpassed by any woman before her - and precious few men as well.
Her associates at school and university - she had few close friends - recall her as industrious, serious-minded, and soberly-dressed, but also possessing what one of them has since described as "an irritating sense of her own superiority".
Inevitably she became head girl at Kesteven and Grantham Girls' High School. She went on a bursary to Somerville College, Oxford, where she read chemistry.
Her principal at Oxford fell short of wild enthusiasm for her abilities, describing her as "a perfectly good second-class scientist".
However, she went on to become only the third woman president of the University's Conservative Association. She continued to work as a chemist until 1954 when she switched to become a barrister specialising in tax cases.
It was in this part of her career that she demonstrated her formidable ability to master a brief and to shame those who had not bothered to do so.
And it was the kind of training which years later made her virtually invulnerable at Question Time in the House of Commons. No matter what subject, however abstruse, was pitched at her, and without previous notice, she dealt with it with total command.
In 1951 she married Denis Thatcher, a shrewd and highly successful industrialist some ten years her senior. Contrary to common belief, Mrs Thatcher never dominated that marriage. Denis, an independent character, carried on with his business life while she pursued her political career.
In a very loving partnership he was intensely proud of her achievements and she was no less touched by his unswerving loyalty to her, his impeccable performance as her consort on official occasions, and his instinctive protectiveness towards her.
That instinct was demonstrated more than once when she faced peril in either over-friendly or faintly menacing crowds surrounding her during her street walkabouts, in scores of countries round the world, particularly in Australia and Turkey.
Mrs Thatcher launched into her battle to get into Parliament by unsuccessfully fighting Dartford - where she met Denis - in 1950 and again in 1951. Their twins, Mark and Carol, were born by Caesarean operation.
She finally entered the Commons in 1959 as Member for Finchley, a seat she represented throughout her career as an MP. The smartly-dressed, brisk and businesslike blonde did not remain unnoticed for long.
She swiftly adapted to the strange ways of Westminster. Her friendly manner and warmth belied and disguised the white heat of her ambition.
Thatcher epitomised then, as she did throughout her career, the self-made woman. Once she said contemptuously: "I owe nothing to Women's Lib" when she was criticised by feminists.
In the final years of the Harold Macmillan-Alec Douglas-Home administrations, Mrs Thatcher was parliamentary secretary, Ministry of Pensions and National Insurance.
Later, Mr Heath, the man she was destined to topple from the Tory leadership, took her into his shadow cabinet in 1966, but not without what turned out to be fateful reservations. He observed uncannily: "Once she's there, we'll never be able to get rid of her."
A quarter of a century later Mr Heath was still brooding moodily over those words.
When the Heath administration took office in 1970, Mrs Thatcher became Education Secretary, a key job in the new cabinet. Here, she worked uneasily. Her natural desire to give people independence and self-reliance was constrained - and had to be - by the collective approach of a Government much more timid than her own administrations were to be.
Even so, she quickly became a hate figure on the Labour benches, branded as "Thatcher the Milk Snatcher" because of her decision to stop free milk for primary schoolchildren.
She also cancelled a Labour circular requesting councils to move towards comprehensive schooling and she attempted to reform student union financing.
She was fast becoming a substantial figure in the Tory hierarchy. People were sitting up and taking notice - and some of her colleagues were already looking decidedly uneasy at the prospect of this by now clearly insatiable political ambition.
The two disasters that befell the Conservatives - general election defeats in February and October 1974 under the uninspiring leadership of Mr Heath - gave Mrs Thatcher the opportunity she so desperately sought.
There was now widespread dissatisfaction with Mr Heath. After that second defeat he sat, crunched up to half his size, a pitiable figure, waiting on a hard wooden bench in the committee corridor of the House of Commons to be told bluntly by the powerful Tory 1922 Committee of backbenchers just what they thought of him.
The word quickly went around that Mrs Thatcher would be bold enough to challenge him. She first consulted her close friend, confidant and even guru, Sir Keith, later Lord Joseph, and was assured that he would not stand. She would never have challenged Heath if Joseph had decided to enter the fray. But he did not.
Opportunities like that come once in a political lifetime. If you miss them, you have missed everything. Mrs Thatcher hurled down the gauntlet - and from that moment Heath was a beaten, resentful and doomed man.
It is arguable that if she had not been so intrepid, none of her timid colleagues would have dared to challenge him. Indeed some waited until she had smashed Heath out of the running before plucking up the courage to enter the fray themselves.
But by now she was the darling of Tory rank-and-file MPs sickened by what they regarded as the wishy-washy Heath brand of Conservatism. They were struck with admiration at her valour.
She made short work of defeating the lugubrious, lovable Willie Whitelaw - he wept when he was beaten - who epitomised languor and lethargy. And so, in 1975 she became the first woman at the helm of the Conservative Party, hell-bent on seeing the Tories back in power.
Her principal lieutenant in that leadership election campaign was Airey Neave, who was tragically assassinated by the IRA in March, 1979, only months before she came to power.
She was shattered by the news, but his death served only to increase her resolution to crush terrorism, to offer terrorists no quarter, to do no deals with them. She regarded them as vicious criminals, not political partisans.
Later, Mrs Thatcher was to tell a press conference in Saudi Arabia, when questioned about "political" reasons for IRA activity: "A crime is a crime is a crime."
She denounced those who gave the terrorists, in her own striking phrase, "the oxygen of publicity".
So Mrs Thatcher drove in triumph that night in 1975 from the House of Commons to Conservative Central Office where she straightaway set in train an unstoppable campaign whose momentum, four years later, was to pitch her into power.
First Harold Wilson and then his successor James Callaghan quickly found they had a sweetly snarling tigress to deal with at the Despatch Box, compared with the lumbering bear that was Edward Heath.
She injected new heart, spirit and fire into the Conservative Party. Meanwhile Labour staggered from one crisis to another, winding up with the so-called 1978-79 winter of discontent, during which strikers even refused to bury the dead and with the Government seemingly impotent to act.
To crown it all Callaghan returned to the grime and snow of strike-ravaged Britain from an indulgent summit in the tropical sunshine of Guadeloupe and was reported as saying: "Crisis? What crisis?"
The words were, in fact, a headline in the following day's Sun newspaper. But from that moment on he, too, was a doomed man.
Within months, Mrs Thatcher, aged 53, was stepping into Downing Street, softly quoting from memory the exquisite prayer of St Francis of Assisi: "Where there is discord, may we bring harmony. Where there is error, may we bring truth. Where there is doubt, may we bring faith. Where there is despair, may we bring hope."
She had belied her prediction seven years earlier, when questioned about the likelihood of there being a woman Prime Minister. She had said then: "I don't think it will come for many, many years. I don't think it will come in my lifetime."
Mrs Thatcher set to work with fervour. As inflation continued to rise, she served notice of the strict monetary policy which she was never to betray.
The state was to be "rolled back" in a huge programme of privatisation. Trade union power was to be curbed and new laws introduced to make it harder to go on strike.
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