Baroness Margaret Thatcher, 87, has died this morning following a stroke, her spokesman Lord Bell said.
He said: "It is with great sadness that Mark and Carol Thatcher announced that their mother Baroness Thatcher died peacefully following a stroke this morning."
Lady Thatcher was Conservative prime minister from 1979 to 1990.
David Cameron called her a "great Briton" and the Queen has spoken of her sadness at the death.
Downing Street said Lady Thatcher would be accorded the same status of funeral as the Queen Mother and Princess Diana, but will not lie in state, in accordance with her own wishes.
In a statement on the Downing Street Twitter feed, Mr Cameron said: "It was with great sadness that l learned of Lady Thatcher's death. We've lost a great leader, a great prime minister and a great Briton."
A Buckingham Palace spokesman said: "The Queen was sad to hear the news of the death of Baroness Thatcher. Her Majesty will be sending a private message of sympathy to the family," it said.
Love or hate her, the former Tory Prime Minister 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 dispatched 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 nation-wide and year-long miners' strike, which threatened to cripple Britain's entire economic base.
Her triumphant achievement of power in May 1979 signaled 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.
For a full tribute, see tomorrow's Grimsby Telegraph.
