Baroness Thatcher has died at the age of 87 after suffering a stroke, her family has announced.
Her son, Sir Mark, and daughter Carol confirmed that she died this morning.
Lord Bell, her spokesman, 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."
Known as the Iron Lady, Margaret Thatcher governed Britain from 1979 to 1990. She will go down in history as Britain's first female prime minister. In quotes: Margaret Thatcher
In response to the news that Lady Thatcher has died aged 87, Mr Cameron said: "It was with great sadness that I learned of the death of Lady Thatcher. We have lost a great leader, a great Prime Minister and a great Briton."
Surrey County Councillor Tim Hall (Conservative, Leatherhead and Fetcham East) added: "I think she was a transformational figure as the first ever female Prime Minister and obviously my thoughts must go to her family.
"She had a terrific influence over the latter half of the twentieth century and she was a truly inspiring figure."
Mole Valley District Councillor James Friend (Conservative, Westcott) said it was a "sad day for Britain".
He continued: "I know plenty of people who agreed and plenty of people who disagreed with what she put through but I think overall she made a very positive contribution to our country and she was statesman-like to the last."
The leader of the Conservative delegation in the European Parliament Richard Ashworth MEP for the South-East said: "Margaret Thatcher was an inspiration leader who transformed the United Kingdom from a country at the behest of the trade unions, into a modern highly skilled competitive economy.
"We owe a great deal to Baroness Thatcher for her leadership and bravery and her legacy can be seen today all over this nation. She was a great patriot, may God rest her soul".
Ed Miliband, the Labour leader, has also paid tribute to Lady Thatcher.
"I send my deep condolences to Lady Thatcher's family, in particular Mark and Carol Thatcher.
"She will be remembered as a unique figure. She reshaped the politics of a whole generation. She was Britain's first woman Prime Minister. She moved the centre ground of British politics and was a huge figure on the world stage.
"The Labour Party disagreed with much of what she did and she will always remain a controversial figure. But we can disagree and also greatly respect her political achievements and her personal strength.
"She also defined the politics of the 1980s. David Cameron, Nick Clegg and I all grew up in a politics shaped by Lady Thatcher. We took different paths but with her as the crucial figure of that era.
"She coped with her final, difficult years with dignity and courage. Critics and supporters will remember her in her prime."
Nick Clegg, the Lib Dem deputy prime minister, 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."
Mr Clegg's tribute came as Lady Thatcher's former colleagues expressed their sadness and hailed her as "a titan of British politics".
Lord Howard of Lympne, one of her successors as Conservative leader, said the former Prime Minister "saved" Britain with her reforms to the economy.
"She was a titan in British politics," he told Sky News. "I believe she saved our country because when she took over in 1979 we were in real economic decline and many thought the country was ungovernable.
"I believe she saved the country, she transformed the economy and I think she will go down in history as one of our very greatest Prime Ministers."
Lord Howard accepted that Baroness Thatcher was also a highly contentious figure but insisted that she could not possibly "have done what needed to be done by consensus".
"There was a need for bold decisions," he said.
"She was immensely considerate and always charming. She certainly expected you to be on top of your job."
Iain Duncan Smith, the work and pensions secretary, has said that Lady Thatcher was the reason he went 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."
Lady Thatcher had become increasingly frail in recent years following a series of small strokes in 2001 and 2002.
Her daughter Carol also revealed in 2008 that she had been diagnosed with dementia, which had increasingly affected her memory for the last decade.
Ill-health had prevented her attending an 85th birthday party in Downing Street arranged by David Cameron in October 2010.
It also prevented her attending the Royal wedding of Prince William and Kate Middleton on April 29, 2011 at Westminster Abbey.
Nigel Farage, the Ukip leader, has said: "I have always said that Mrs Thatcher was a great inspiration to me personally.
"Whether you loved her or hated her nobody could deny that she was a great patriot, who believed passionately in this country and her people.
"A towering figure in recent British and political history has passed from the stage. Our thoughts and prayers are with her family."
Carwyn Jones, the Labour first minister of Scotland, said: "Margaret Thatcher was a major force in British political life who undoubtedly had a significant influence on the political, social and economic landscape in Wales and the UK.
"There's no doubt about her personal achievement as the first woman to become British Prime Minister. Her place in the history books is assured."
Charles Kennedy, the former Lib Dem leader, has said: "In extending sincere sympathy to the Thatcher family we remember today a landmark political figure, both at home and abroad. She was one of those politicians who made the weather.
"As a politically divisive figure - not least where Scotland was concerned - her legacy will always be controversial.
"And she continues to cast a considerable shadow across today's Conservative party.
"But her impact - positive and negative - remains near immeasurable."
Lady Thatcher published two volumes of memoirs. The first, The Downing Street Years (1993), covered her time as Prime Minister, while the second volume, The Path to Power (1995), concerned her early life. She also published a magisterial volume on international affairs, Statecraft (2002).
She is survived by her two children. Her husband Sir Denis died in 2003.
A Downing Street spokesman has said: "Downing Street 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."
