Former Prime Minister Baroness Thatcher has died "peacefully" at the age of 87 after suffering a stroke, her family has announced.
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.Obama tribute
Mr Cameron, who is in Madrid for meetings, has cancelled planned talks in Paris with French President Francois Hollande and will return to the UK later on Monday.
BBC political editor Nick Robinson said Lady Thatcher had been a controversial politician who inspired "passion" among both 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.8 April 2013 - Dies after suffering a stroke
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.