This was a radical rightwing government before the reshuffle toughened up its Thatcherite credentials. From the start, David Cameron's mission was to break the postwar consensus on the welfare state that survived Margaret Thatcher. Where she privatised state-run industries, the Cameron government would dismantle the state itself. As students they hung posters of her on their walls. Now they go where she never dared – not boldly declaring it before the election, but hell-for-leather lest they only get one term.

Yet here is the Tory party in turmoil, blaming its poor poll ratings on Cameron's lack of spine. Some seem so desperate to hold on to their seats that they even imagine the egotistical exhibitionist Boris Johnson as a saviour. How bizarre are these stirrings from the party's right. Last week Liam Fox and David Davis launched Conservative Voice, clamouring about Europe, lower taxes and deregulation, while backbench young turks of the Free Enterprise Group published Britannia Unchained, calling for much the same while abusing British workers as "the worst idlers in the world".

Among the few still deceived by Cameron's soft-centred pre-election disguise are his own backbenchers. Stupidity is the only explanation. The idea that they are saddled with some milksop centrist kowtowing to the Liberal Democrats defies the most cursory glance at the Cameron record so far.

This week in our new book, Dogma and Disarray – Cameron at Half-Time, David Walker and I publish an interim report. As with our books on the Labour parliaments, culminating in The Verdict on Labour's 13 years, we follow the facts on the ground, the policies carried out, avoiding the political noise at Westminster. Politicians' characters are intriguing, but what matters is what they do.

When Cameron assumed leadership of a party that had lost three elections, the focus groups warned him to embrace welfare state values. Or at least to pretend to. How consciously he dissembled we don't know, perhaps he doesn't either. He retains the misleading aura of a pragmatist, disguising the fervour of his anti-state dogma. He may be no great ideas man, but for his Tory generation it's a reflex: they instinctively breathe free-market Hayek and Schumpeter on "creative destruction", applying it to government itself. Their Americanism takes the form of shipping in Tea Party Republicanism – how readily they would have let Murdoch create a British Fox News.

Only dogma explains why Cameron risks all by stripping down the NHS, Britain's holy of holies. The only serious obstacle to his intent has been his own ineptitude at implementation. Yet for all the bungled U-turns, there has been no deviation from the great austerity.

How ironic that he should be assailed from his right. In misleading voters as to his intentions before the election, he seems not to have let his own party into the secret. They only heard they were to be disinfected, detoxified, turned green and never be nasty again. The reality of spending cuts the Institute for Fiscal Studies calls "almost without historical and international precedent" seems to pass by the likes of Fox and Davis.

Let's reprise Cameron's audacity. Start with "I will cut the deficit, not the NHS", and "no top-down reorganisation". In office he has encouraged not just cuts but tumultuous change and wholesale outsourcing, this week with another £20bn worth of the NHS up for market bidders. How odd that the right fails to appreciate the radicalism of what will be permanent rupture. Cameron's Open Public Services white paper revealed "any qualified provider" as the template for universal outsourcing.

If his pre-election "equality" soundbites made his right wing queasy, in office Cameron has proved as anti-woman as any reactionary might wish: promising a third of his ministers would be women, he appointed only 23 out of 121. He promised "the most family-friendly government ever", and "a more civilised work-life balance", amid pictures of him cooking his children's breakfast. Yet the IFS finds mothers and children hit hardest, the child trust fund abolished, and tax credits, childcare, Sure Start and much more cut. On child benefit, Cameron said, "I wouldn't means-test it", but he did. Education maintenance allowance would be kept: it's gone. Thousands more midwives were promised, none were delivered. He signed the pledge on child poverty, yet the IFS predicts half a million more poor children. He said, "I'd never do anything to damage disabled children": two-thirds will lose Disability Living Allowance.

Big Society? Charities have suffered swingeing grant cuts. No rise in VAT, he promised; it rose. How his party hated him hugging hoodies – but now community sentencer Ken Clarke is replaced with prison-addict Chris Grayling, and G4S wins the contracts. Vote blue, go green? The new windmill-hating energy and climate secretary supports the dash for gas, cutting renewables.

Days before the election Cameron said: "Any minister who comes to me and says here are my plans and they involve frontline reductions, they'll be sent straight back to their department to go away and think again." Tell that to the nurses and police whose ranks have shrunk by thousands. Why aren't the right satisfied when "We're all in this together" turned out to mean £14,000 tax cuts for millionaires? Or that 10,000 HMRC staff are cut from catching tax-dodgers?

The party's trouble springs not from a lack of rightwing zeal but from failed austerity medicine, and the polls are grim. Cameron pledged national debt would be falling as a percentage of GDP by 2015: it won't. Instead the Office for Budget Responsibility says net debt will rise by £465bn. That's more than the £319bn it rose in all of Labour's 13 years.

Tory turbulence is nothing new. Any sign of weakness and they shoot their leaders with a ruthlessness absent from Labour's tradition. If he looks like a winner, they will let Boris Johnson break any precedent he likes. If enough MPs reckon he can save their seats, they'll have him, egomania and all. The public are deceived again if they fall captive to Johnson's wit, let alone the preposterous pretence to be an "outsider". They'll find him cut from identical ideological cloth as the Cameron circle: he's no maverick. And for all his dog-whistling to the right, it's implausible he could offer them more than Cameron, at the head of the most rightwing of all postwar governments.

Dogma and Disarray – Cameron at Half-Time, by Polly Toynbee and David Walker, is available from guardianbookshop.co.uk

• This article was amended on 18 September 2012. The original said the Institute for Fiscal Studies had described welfare cuts as "without historical and international precedent". In fact it described overall spending cuts planned by the government as "almost without historical and international precedent".