Her spokesman Lord Bell said: "It is with great sadness that Mark and Carol Thatcher announced that their mother Baroness Thatcher died peacefully following a stroke this morning."
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A statement from Buckingham Palace said the Queen was "sad" to hear the news and had sent a private message of sympathy to the family.
David Cameron immediately cut short his trip to Europe, saying the country had lost "a great leader, a great Prime Minister and a great Briton".
He ordered the union jack above Downing St to be flown at half mast. Baroness Thatcher became known as The Iron Lady during three consecutive terms in the residence, elevating it to the status of the White House or the Kremlin.
The Conservative politician served as British leader from 1979 to 1990. She first entered Parliament in 1959 as MP for Finchley, north London and led her party after unseating Edward Heath in 1975.
As the occupant of Number 10, Baroness Thatcher presided over many of the key moments in British history including the Falklands War, the Miners' Strike and the end of the Cold War.
Indeed, it was her role in bringing about the West's victory in the Cold War along with her friend US President Ronald Reagan that led a Soviet commentator to give the leader her flinty sobriquet.
Although a controversial figure because of her uncompromising style and policies, she is also widely regarded as the foremost post-war prime minister.
From her early beginnings as a grocer's daughter, she became a giantess of politics, bestriding the world of Westminister and far, far beyond with her trademark Aspreys handbag.
Born on 13 October 1925, she was the daughter of Alfred and Beatrice Roberts, who owned two shops, one of which the family lived above.
Her father, a local Methodist preacher, inspired an early interest in politics when he became Mayor of Grantham in 1945. By that time the young Margaret was studying chemistry at Somerville, College Oxford.
With so many women in positions of authority now, it's easy now to underestimate the achievements of this early exponent of girl power.
She combined marriage to her devoted husband Denis Thatcher with studying for her bar exams and bringing up their twins Carol and Mark. In 1953, the year they were born Mrs Thatcher qualified as a barrister, specialising in tax.
A wealthy businessman, "her marvellous husband" supported her during the early days of her political career and was her rock once it took off. He was, she said, "the golden thread" running through her life and he later would be knighted in recognition of his achievements.
Of their union, Carol once said: "They had a unique relationship, a partnership that was way ahead of its time, a two-career household, an understanding of love and loyalty – loyalty was so important to my mother – and very little friction."
By 1970, her mother was Secretary of State for Education. From there it was a logical step to go for the 'top job'. The energetic premier hated references to her gender, but there was no doubt she used feminine wiles to deal with being in a man's world.
With her ministers she was one part stern headmistress, one part mother and one part flirt. They responded with the tremendous loyalty that she demanded until her resignation was forced by a backroom coup in 1990, which saw her leave her beloved Downing St in tears.
The Baroness will not have a state funeral, as had been previously reported. This honour has only previously been granted to four other prime ministers, among them Winston Churchill.
Instead ,she will be laid to rest with full military honours – a similar send off to those for Princess Diana and the Queen Mother. The ceremony will take place in St Paul's Cathedral.