Margaret Thatcher, the most dominant British prime minister since Winston Churchill in 1940 and a global champion of the late 20th-century free market economic revival, has died.

Her spokesman, Lord Bell, said on Monday: "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."

Downing Street announced that she would receive a ceremonial funeral with military honours at St Paul's Cathedral.

David Cameron, who is cutting short his trip to Europe to return to London following the news, 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."

He told the BBC: "As our first woman prime minister, Margaret Thatcher succeeded against all the odds, and the real thing about Margaret Thatcher is that she didn't just lead our country, she saved our country, and I believe she will go down as the greatest British peacetime prime minister."

Cameron later said parliament would be recalled on Wednesday "for a special session in which tributes will be paid" to Lady Thatcher.

In a statement, President Barack Obama said that, "the world has lost one of the great champions of freedom and liberty, and America has lost a true friend."

"Here in America, many of us will never forget her standing shoulder to shoulder with President Reagan, reminding the world that we are not simply carried along by the currents of history—we can shape them with moral conviction, unyielding courage and iron will."

He added that her premiership was "an example to our daughters that there is no glass ceiling that can't be shattered".

Buckingham Palace said the Queen was sad to hear the news and that she would be sending a private message of sympathy to the family.

The first woman elected to lead a major western state, Lady Thatcher, as she became after the longest premiership since 1827, served 11 unbroken years at No 10. She was only overthrown by an internal Tory party coup in 1990 after her reckless promotion of the poll tax led to rioting in Trafalgar Square.

Thatcher, who was 87, had been in declining health for some years, suffering from dementia. The death of Sir Denis Thatcher, her husband of 50 years and closest confidante, intensified her isolation in what had proved a frustrating retirement, despite energetic worldwide activity in the early years.

After a series of mini-strokes in 2002 Thatcher withdrew from public life, no longer able to make the kind of waspish pronouncements that had been her forte in office – and beyond.

Her death was greeted with tributes from across the political spectrum.

As Labour sources announced the party would suspend campaigning in the local election as a mark of respect, its leader, Ed Miliband, said: "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."

The deputy prime minister, 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."

The work and pensions secretary, Iain Duncan Smith, 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."

The former prime minister Tony Blair said: "Margaret Thatcher was a towering political figure. 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."

Blair's successor as prime minister, Gordon Brown, said: "She will be remembered not only for being Britain's first female prime minister and holding the office for 11 years, but also for the determination and resilience with which she carried out all her duties throughout her public life. Even those who disagreed with her never doubted the strength of her convictions and her unwavering belief in Britain's destiny in the world."

Describing her as a political phenomenon, the former Tory prime minister Sir John Major said: "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."

The mayor of London, Boris Johnson, said: "Her memory will live long after the world has forgotten the grey suits of today's politics."

The "Iron Lady" proved a significant cold war ally of the US president Ronald Reagan in the final showdown with the Soviet Union, which broke up under reformist pressures led by Mikhail Gorbachev, a Kremlin leader with whom Thatcher famously declared she could "do business".

As a result, many ordinary voters in ex-Soviet bloc states saw her as a bold champion of their liberty, a view widely shared across the spectrum of mainstream US opinion – though not at home or among key EU partners.

Thatcher was an unremarkable mid-ranking Conservative politician – known chiefly for being a "milk-snatching" education secretary under Edward Heath (1970-74) – until she unexpectedly overthrew her twice-defeated boss to become party leader in 1975.

Within a decade she had become known around the world – both admired and detested – for her pro-market domestic reforms and her implacable attitudes in foreign policy, including her long-running battle with the IRA, which almost managed to murder her when it placed a bomb in the Grand Hotel, Brighton, in 1984.

At home the emerging doctrine of Thatcherism meant denationalisation of state-owned industry – the new word "privatisation" came into widespread use in many countries – and defeat of militant trade unionists, notably the National Union of Miners, whose year-long strike (1984-85) was bitter and traumatic.

Boosted by the newly arrived revenues from Britain's North Sea oil fields, Thatcher had room to manoeuvre and change the ageing industrial economy in ways denied to postwar predecessors, and she used the opportunity to quell her enemies – including moderate "wets" in her own party and cabinet.

But she also deployed her notorious "handbaggings" in the European Union to obtain a British rebate – "my money" as she called it. She was less successful in fending off the centralising ambitions of the "Belgian empire", her description of the European commission, especially in the years when it was headed by the French socialist Jacques Delors.

A further sign of her losing her grip came when Thatcher, long a sympathiser with the apartheid regime in South Africa against the liberation movement, dismissed Nelson Mandela as a terrorist.

Her allies in the tabloid press, notably Rupert Murdoch's Sun, egged her on. And, as the British economy recovered from the severe recession that her monetarist medicine had inflicted on it – to tame the unions and cure inflation – she briefly seemed invincible.

But untrammelled power, with the defeat or retirement of allies who had kept her in check, led to mistakes and growing unpopularity. When Sir Geoffrey Howe, nominally her deputy, finally fell out with Thatcher – chiefly over Europe – his devastating resignation speech triggered Michael Heseltine's leadership challenge.

It had been expected since he resigned as defence secretary over the Westland helicopter affair in 1986, Thatcher's closest previous brush with political death.

Heseltine denied her outright victory in the first round of voting – then confined only to MPs – and she made way for Major rather than risk losing to him in the second ballot.

In retirement she wrote highly successful memoirs in two volumes and campaigned energetically on behalf of the Thatcher Foundation, which sought to promote her values – free markets and Anglo-Saxon liberties – around the world. Speaking engagements made her moderately wealthy and she made her final home in London's Belgravia.