Baroness Thatcher died on Monday following a stroke, her spokesman Lord Bell has announced.
The former Prime Minister, who was 87, had suffered from prolonged ill health in recent years.
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.
“A further statement will be made later.”
Baroness 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.
In a statement on the Downing Street Twitter feed, Prime Minister David 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.”
Buckingham Palace said the Queen is sad to hear the news and will be sending a private message of sympathy to the family.
Labour leader Ed Miliband said Baroness Thatcher would be remembered as “a unique figure”, adding: “She reshaped the politics of a whole generation.”
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.”
Former Prime Minister Tony Blair described her as “a towering political figure”.
He added: “Very few leaders get to change not only the political landscape of their country but of the world. Margaret was such a leader.
“Her global impact was vast. And some of the changes she made in Britain were, in certain respects at least, retained by the 1997 Labour Government, and came to be implemented by governments around the world.”
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.”‘Force of nature’Former Conservative prime minister Sir John Major described Baroness Thatcher as a “true force of nature” and a “political phenomenon”.
He said: “In government, the UK was turned around under and in large measure because of her leadership.
“Her reforms of the economy, trades union law, and her recovery of the Falkland Islands elevated her above normal politics, and may not have been achieved under any other leader.
“Her outstanding characteristics will always be remembered by those who worked closely with her: courage and determination in politics, and humanity and generosity of spirit in private.”
First Minister Alex Salmond said: “Margaret Thatcher was a truly formidable prime minister whose policies defined a political generation.
“No doubt there will now be a renewed debate about the impact of that legacy. Today, however, the proper reaction should be respect and condolences to her family.”
Scottish Conservative leader Ruth Davidson said: “Baroness Thatcher was a true Conservative revolutionary challenging outdated institutions, confronting vested interests and transforming Britain into a property-owning democracy.
“She empowered millions of people in a way that was previously unimaginable and the positive impact of her legacy with be felt by thousands of families for decades to come.
“In becoming Britain’s first woman prime minister and winning three consecutive elections, she didn’t so much smash the glass ceiling as blow it to pieces.She proved to women everywhere there was nothing they couldn’t accomplish.
“Baroness Thatcher defended Britain’s sovereignty against opposition both at home and internationally and re-established Britain’s reputation on the world stage, and the whole of the free world should be grateful for the crucial role she played in the downfall of Communism.
“She will go down in history as one of the truly great prime ministers.”
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.”‘A great day’ for minersHowever, David Hopper, the general secretary of the Durham Miners’ Association, said it was a “great day” for coal miners.
The ex-miner, who turned 70 today, spent all of his working life at Wearmouth Colliery.
He said: “It looks like one of the best birthdays I have ever had.There’s no sympathy from me for what she did to our community. She destroyed our community, our villages and our people.
“For the union this could not come soon enough and I’m pleased that I have outlived her.It’s a great day for all the miners I imagine we will have a counter demonstration when they have her funeral.
“Our children have got no jobs and the community is full of problems. There’s no work and no money and it’s very sad the legacy she has left behind.
“She absolutely hated working people and I have got very bitter memories of what she did. She turned all the nation against us and the violence that was meted out on us was terrible.
“I would say to those people who want to mourn her that they’re lucky she did not treat them like she treated us.”
A Number 10 spokesman said: “We can announce that, with the Queen’s consent, Lady Thatcher will receive a ceremonial funeral with military honours.
“The service will be held at St Paul’s Cathedral. A wide and diverse range of people and groups with connections to Lady Thatcher will be invited.
“The service will be followed by a private cremation.All the arrangements being put in place are in line with wishes of Lady Thatcher’s family. Further details will be published over the coming days.”
Mr Cameron is returning early from an official trip to Spain.For an in-depth study of Baroness Thatcher’s legacy, and a look back on her visits to Courier country, see Tuesday’s paper or try our digital edition.