On 11 May, David Cameron succeeded Gordon Brown as Prime Minister, taking the helm of the country's first coalition government since 1945 - not to mention being, at the age of 43, the youngest British leader since Lord Liverpool in 1812. On 18 August, Cameron will mark his first 100 days in office. Critics and supporters alike would agree that the new Prime Minister has presided over a frenetic few months. The much-mocked Tory election slogan "Vote for change" has been borne out: there has been change aplenty, change enough.

So, how should we judge Cameron's initial period in power? The notion of the "first 100 days" was pioneered as a measure of American presidential dynamism by Franklin Delano Roosevelt when he took office in 1933, in the midst of the Great Depression. It has since become a symbolic, if artificial, benchmark for assessing the early successes of a US president - successes personified by FDR himself, who pushed 15 major bills through Congress in his first 100 days.

“I do not see how any living soul can last physically going the pace that he is going," said Senator Hiram Johnson of FDR at the time, "and mentally any one of us would be a psychopathic case if we undertook to do what he is doing."

David Cameron, like FDR before him, understands that leaders have limited windows of opportunity to effect real change after winning elections and taking office - and Cameron did not even win an election. Nonetheless, ensconced inside No 10, with the support of Nick Clegg and the Liberal Democrats, he has moved at confident speed. The Queen's Speech on 25 May - which the Prime Minister accurately described as a "radical programme for a radical government" - unveiled 23 bills (and one draft bill) detailing ambitious plans for major reform of schools, welfare, the police and the political system. Every week brings another policy, proposal or white paper.

“Shock and awe, we should remember, is Cameron's style," says Professor Tim Bale, author of The Conservative Party: from Thatcher to Cameron. "It's exactly what he did when he became leader of the party in late 2005. The aim was - and is - to show people he's hit the ground not just running, but sprinting, to symbolise a big shift and show he's there to make a difference."

This, however, is as far as the comparison with Roosevelt goes. The latter's presidency rescued the United States from depression; Cameron's premiership risks sending Britain back into recession. While FDR used his first 100 days to extend the remit of the US federal government - boosting employment through public works, regulating banking and Wall Street, providing support for agriculture and labour - Cameron has used his to set about ­dismantling the British welfare system and rolling back the state; to make changes which, as he remarked in a speech on 7 June, "will affect our economy, our society - indeed, our whole way of life".

The Secretary of State for Education, Michael Gove, has hinted that profit-making companies will be allowed to run new "free schools" in England, set up by parents outside of local authority supervision. The Secretary of State for Health, Andrew Lansley, has set in motion the "denationalisation" of the National Health Service by handing over the budget for hospital care to family doctors, and encouraging hos­pitals to attract more private patients from home and abroad. The Secretary for Work and Pensions, Iain Duncan Smith, has launched an assault on the benefits system, including swingeing cuts to housing benefit that threaten to make hundreds of thousands of poor families homeless.

We cannot say we were not warned. In his speech to the Conservative party conference in October 2009, Cameron declared that his mission as prime minister would be to tear down so-called big government. The phrase "big government" appeared 14 times in that one speech, in which, studiously ignoring the role played by bankers in causing the worst financial crisis in living memory, he claimed: "It is more government that got us into this mess."

Despite appearances to the contrary, Cameron is less a Whiggish pragmatist than a radical, in the Margaret Thatcher mould. His combination of market-oriented reforms to the public sector and savage cuts to public spending - hailed by the investment bank Seymour Pierce as heralding a "golden age of outsourcing" - suggests that he is intent on completing the neoliberal, state-shrinking revolution that Thatcher began and which Tony Blair and Gordon Brown did little to reverse.

Cameron's right-wing instincts on the economy, however, have never been properly acknowledged by a press pack beguiled by his “rebranding" of the Conservative Party and distracted by his "progressive" stance on gender, sexuality and race issues, as well as his self-professed passion for civil liberties and the environment. In fact, for far too long, it has been fashionable for commentators on left and right either to belittle Cameron as a man of no substance, a spin merchant, a PR man, a "simulacrum" (to quote the former Tory MP George Walden, writing on these pages in June), or to praise and admire him as a pragmatist, a centrist, a "moderate" in the "One Nation" mould of Benjamin Disraeli and Harold Macmillan.

Disregard the rhetoric and image, and consider instead the record: in his first 100 days, Cameron has gone further than Thatcher - and much faster, too. His "modernising" ally and minister for the Cabinet Office, Francis Maude, has said that the Tories always planned to outstrip the Iron Lady.

“If you look at the last transitions of governments, and the way they came in, I would say one of the things that Thatcher regretted was not pushing ahead vigorously enough, and quickly enough, in terms of reform," Maude said. "The big reforming Thatcher governments were not until 1983 and 1987."

But the big, reforming Cameron government has arrived here and now. That the Prime Minister sits in coalition with Nick Clegg and the Liberal Democrats is irrelevant. The latter may be a centre-left party but it is, as Richard Grayson, vice-chair of the Lib Dems' Federal Policy Committee, has argued, "being led from the centre right". Clegg, like Cameron, has voiced his admiration for Thatcher and, in particular, for her victory over the trade unions in the 1980s. Meanwhile, the Liberal Democrat members of cabinet control none of the front-line, big-spending government departments. Cameron has filled the Treasury, the Foreign Office, the Home Office, the Ministry of Defence and the Department for Work and Pensions with Tories.

“I think Cameron has a huge advantage over Thatcher, in that, at least as far as the Conservative Party component of the coalition goes, he has for the most part got the people he wants in the posts he wants them in," says Bale. "She was much more constrained early on by the need to give jobs to big beasts she didn't agree with or thought were hopeless. There aren't too many of those in the cabinet now."

In his zeal to cut an already falling deficit and "balance the books", for example, Cameron and his Chancellor, George Osborne, have delivered £40bn of tax rises and public spending cuts on top of the £73bn target they inherited from Gordon Brown and Alistair Darling. In the US, cutting the deficit may be a medium-term challenge, but here in the UK, for the Cameron-led coalition, it has become an obsession - "the most urgent issue facing Britain", according to a letter sent by Cameron and Clegg to their cabinet colleagues on 2 August.

Inside the space of 50 days, and behind the cover of an "emergency" and "unavoidable" Budget, Cameron and Osborne have taken one of the biggest macroeconomic gambles of any prime minister and chancellor to have entered Downing Street.

Robert Skidelsky, the cross-bench peer and biographer of J M Keynes, tells me that the Budget was bold, but boldly wrong. "It assumes that determined fiscal tightening will restore confidence and produce a private-sector boom. I believe it will damage confidence and produce a double-dip recession ... Unless the policy is reversed, it will wreck the coalition, increase social conflict and damage the country."

But the Prime Minister, who has announced the deepest and fastest cuts in public spending in living memory, has claimed that his Budget will "protect the poor". The Institute for Fiscal Studies disagrees, describing the "overall impact" of Cameron's economic measures as "regressive" and calculating that his cuts will affect poorer households "significantly harder than richer households". This is the harsh Cameronomics of the coalition.

Next comes the Comprehensive Spending Review, in October, which will set out detailed plans to slash departmental spending by at least a quarter over the next five years. Such fiscal sadism is without precedent. Indeed, it is often forgotten that during Thatcher's premiership public spending grew in real terms by 1.1 per cent a year on average.

For now, Cameron's political honeymoon continues. His approval ratings are high, and the public seems to have accepted the need for "austerity". But what happens when voters start to feel the pinch? Commenting two days after the Budget, on 24 June, the pollster Peter Kellner rightly struck three cautionary notes: "First, the measures have been announced but not yet implemented; second, we do not yet know which specific public services will feel the pain of spending cuts; third, we don't yet know whether the economy will keep growing or slip back into recession." He added, ominously: "Public attitudes a year from now may be very different."

Tony Blair once denied that New Labour was "Mrs Thatcher with a smile instead of a handbag". It is difficult to conceive of a more apt description of David Cameron. Confident, charming, eloquent and telegenic, he has moved effortlessly from opposition into government. Whether it is standing beside Barack Obama in the White House, or berating Harriet Harman from the despatch box in the Commons, he exudes authority. And, in perhaps the high point of his first 100 days, his response to the Saville report on Bloody Sunday was rightly lauded by commentators from across the political spectrum. "For me, it was his People's Princess moment," says Bale, "a pitch-perfect statement that spoke for the country as a whole, irrespective of whether they'd voted for him or not."

Speaking for the "country as a whole" is one thing; governing in the national interest is quite another. It took Thatcher two years to hit her stride, with an austerity Budget in 1981 that led in fairly short order to widespread social discord, followed by public-sector strikes and a long, violent confrontation with the trade union movement. Cameron, by contrast, hasn't waited that long. His desire for cuts in his first three months in office has provoked the unions to begin preparing for national days of protest and co-ordinated industrial action against the government's spending review in October. Union leaders have promised "the biggest public mobilisation since the anti-poll-tax movement". That way riots beckon.

“In the 100 days from March to June [1933]," wrote the American journalist Walter Lippmann, in the wake of FDR's reforms, "we became again an organised nation, confident of our power to provide for our own security and to control our own destiny."

In August 2010, few observers of David Cameron's first 100 days, even in the Prime Minister's loyal inner circle, would make a comparable claim. But it cannot be said often enough: Cameron, like FDR, is a radical. For Roosevelt, his first 100 days were, in the words of the historian Arthur Schlesinger, "only the start of a process that ended by transforming American society". Without a proper mandate, with potentially appalling economic and social consequences, but with a smile on his face, David Cameron has begun a process to do the same to Britain.