Former Prime Minister Baroness Thatcher has died "peacefully" at the age of 87 after suffering a stroke while staying at the Ritz hotel in central London.
David Cameron called her a "great Briton" and the Queen spoke of her sadness at the death.
Lady Thatcher was Conservative prime minister from 1979 to 1990. She was the first woman to hold the role.
She will not have a state funeral but will be accorded the same status as Princess Diana and the Queen Mother.
The ceremony, with full military honours, will take place at London's St Paul's Cathedral.
The union jack above Number 10 Downing Street has been lowered to half-mast while Parliament will be recalled from its Easter recess on Wednesday to enable MPs to pay tributes to the former prime minister.
After cancelling planned talks in Paris with French President Francois Hollande and returning to the UK, Mr Cameron made a statement outside No 10 in which he described Lady Thatcher as "the patriot prime minister" and said she had "taken a country that was on its knees and made it stand tall again".
"Margaret Thatcher loved this country and served it with all she had. For that she has her well-earned place in history - and the enduring respect and gratitude of the British people," he said.
Lady Thatcher, who retired from public speaking in 2002, had suffered poor health for several years. She had been staying at the Ritz hotel since being discharged from hospital at the end of last year.
BBC political editor Nick Robinson said Lady Thatcher - whose husband Denis died in 2003 - had been a controversial politician who inspired "passion" among her critics and supporters.
Her government privatised several state-owned industries and was involved in a year-long stand-off with unions during the Miners' Strike of 1984-5. She was also in power when the UK fought a war following Argentina's invasion of the Falkland Islands in 1982.
Lady Thatcher survived an assassination attempt in 1984, when the IRA bombed the Brighton Grand Hotel, where she was staying for the Conservative Party's annual conference.
During her later years in office she became increasingly associated with Euroscepticism. She is also seen as one of the key movers behind the fall of communism in eastern Europe.
She stood down in 1990 after she failed to beat Michael Heseltine by enough votes to prevent his leadership challenge going into a second round.
World leaders and senior UK figures have been paying tribute to Lady Thatcher.
US President Barack Obama said the world had "lost one of the great champions of freedom and liberty" and that "America has lost a true friend".
German Chancellor Angela Merkel said she would "never forget her part in surmounting the division of Europe and at the end of the Cold War".
Ahead of his return to the UK, Mr Cameron told the BBC: "Margaret Thatcher succeeded against all the odds. The real thing is she didn't just lead our country; she saved our country.
"I believe she will go down as the greatest British peacetime prime minister."
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."
Lady Thatcher was born Margaret Roberts, the daughter of a shopkeeper and Conservative councillor in Grantham, Lincolnshire, in 1925.
She studied chemistry at Oxford University and worked for a plastics company before marrying businessman Denis Thatcher in 1951.
She gave birth to twins Mark and Carol in 1953, the year she also qualified as a barrister, and served as MP for Finchley, north London, from 1959 to 1992.
Having been education secretary, she successfully challenged former prime minister Edward Heath for her party's leadership in 1975 and won general elections in 1979, 1983 and 1987.
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Sir John Major, who replaced Lady Thatcher as prime minister in 1990, called her a "true force of nature".
He added: "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."
Former Labour Prime Minister Tony Blair called her a "towering figure", while his successor Gordon Brown praised her "determination and resilience".
Labour leader Ed Miliband said Lady Thatcher had been a "unique figure" who "reshaped the politics of a whole generation".
He added: "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."
Deputy Prime Minister Nick Clegg described Lady Thatcher as one of the "defining figures in modern British politics", adding: "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."
Others to pay tribute included former chancellors Lord Howe and Lord Lawson, who resigned from her government following differences over economic policy, Europe and her leadership style. Lord Howe said the former prime minister was a "remarkable person" and a "very good" leader.
London Mayor Boris Johnson said Lady Thatcher's memory would "live long after the world has forgotten the grey suits of today's politics" while Scottish First Minister Alex Salmond described her as "a truly formidable prime minister whose policies defined a political generation".
But Lady Thatcher's economic policies and political style also came in for criticism.
Former Labour leader Neil Kinnock said income inequality had grown sharply during her time in office while Sinn Fein president Gerry Adams said she had "prolonged the war and caused great suffering" in Northern Ireland by the use of "draconian, militaristic policies".
In a statement, The National Union of Mineworkers said Lady Thatcher had "set out to serve those whose interests were profit for the few" and this had led to the "decimation" of the coal industry.
And "parties" have been taking place in Glasgow and in Brixton, south London, to mark Baroness Thatcher's death. BBC reporters said about 250 people are attending the event in Glasgow and 100 in Brixton.