Dominic Lawson: Cameron is facing class war, in his own party

Nadine Dorries's curriculum vitae is everything David Cameron says he wants to encourage in the "modern, compassionate Conservative Party". The Tory MP for Mid-Bedfordshire was for many years a nurse in the NHS; she is a Liverpudlian, comprehensive-educated, and grew up on a council estate.

Perhaps that is part of the reason why so many were offended on her behalf when in the House of Commons, David Cameron described her as "frustrated" – and then sat down, giggling, amid gales of laughter from other male MPs. Although the charge against Cameron was one of condescension to a woman (for which he later apologised), others on the Conservative benches interpreted it somewhat differently: one described it as "the worst of the Bullingdon [Club]". This remark encapsulated what a dangerously large number of Tory backbenchers feel: that their leader is still at heart the Old Etonian upper-class bon vivant, utterly disconnected from the concerns of the working families that they as a party should represent.

It is in this context that the departure of Liam Fox has a social as well as a political fallout. Fox, like Dorries, is from a family that first acquired a home directly as a result of Margaret Thatcher's "right to buy" for council-house tenants. State-educated, and a graduate of Glasgow Medical School, Dr Fox was widely seen as the purest example of the Thatcherite spirit in David Cameron's cabinet.

Yet although Fox himself was not the leader of any faction within the Conservative Party, there are many – not least among the new 2010 intake – who can be described as "Thatcher's children". Like her, they identify completely with the striving middle classes and see those interests as inseparable from the interests of the nation as a whole. They were inspired by her example of turbo-charged meritocracy and share her thinly disguised contempt for the old social elites, which they regard as decadent and even unpatriotic (Fox would emphasise this by his habit of wearing Union Jack cufflinks, which one can't imagine Cameron doing except as a publicity stunt at a national sporting event).

Although Thatcher herself rarely gave public vent to these emotions, it was illuminated some years ago in a television interview with the retired Foreign Office panjandrum Sir Anthony Parsons, who recorded her saying to him: "Do you know, Tony, I am so glad that I don't belong to your class." When Parsons asked "What class would that be, Prime Minister?" she retorted "The upper-middle class who can see everybody's point of view but have no view of their own."

In a sense, that was the charge that Dorries had been laying against Cameron, although the context was her accusation that a Tory-led government is too much under the influence of the Liberal-Democrat minority partner. There are many others, much more influential than Ms Dorries, who share this opinion. Graham Brady, the articulate chairman of the 1922 Committee of Conservative backbenchers, Andrew Tyrie, the forensically bright chairman of the House of Commons Treasury Committee and John Redwood, whose online diary is required reading among the Tory grassroots, are all of this view.

Tyrie was the first of his family to attend University; Brady and Redwood are both grammar school-educated – and like many of their colleagues were appalled by Cameron's scrapping of the traditional Tory support for selective education within the state sector. The way they see it, the privately educated coterie around Cameron – who could easily afford to send their children to eye-wateringly expensive independent schools – were shockingly indifferent to the value (socially as well as financially) of grammar schools to the aspirant lower-middle classes.

In the spirit of Thatcher's remark to Sir Anthony Parsons, such Tories wonder what David Cameron really believes in, other than a natural right to rule. It was the Economist that best captured this objection, just before the general election: "Mr Cameron epitomises British elites: he understands his high-earning peers and feels a genuine noblesse oblige towards the poor, but the people in between are somehow beyond his ken."

It is fair to say that the Tory leader, more than anyone, is desperately concerned about this impression being given. In the televised general election debates between the party leaders, he was embarrassingly insistent on portraying his family as "ordinary", and in the first of them on three occasions told the audience his children were at state schools, even though no one from the audience had asked.

Yet Cameron went too far for his old acquaintance from Brasenose College Oxford, Toby Young, when he described himself and his wife Samantha as from the "middle-classes": "Hang on a minute. Cameron was educated at Eton and is reportedly worth £30m. His wife is the daughter of a baronet and the stepdaughter of a Viscount. If they're 'middle class' what does that make me?" Toby should know that it is not done among the upper-classes to describe themselves as anything other than middle-class. Put it down to self-preservation, or even an acquired faux-modesty; and besides, Cameron could point out that he comes from a long line of stockbrokers, not landed gentry.

More to the point, Cameron does show signs of understanding the day-to-day concerns of those who have to scrape to get by. That, at least, is my take on his decision last week to infuriate the health lobby by not acceding to its demand that we follow the Danes with a special tax on "unhealthy food". If there was one thing which would have condemned Cameron as hopelessly out of touch with "ordinary people", it would have been a levy on hamburgers and chips.

For similar reasons, the Tory backbenches increasingly regard as politically suicidal the idea of new "green" taxes on fossil fuel consumption (beloved of the Liberal Democrats). Thus, Nadine Dorries let rip on Conservative Home website at the weekend: "No mother will forgive Cameron if she is unable to provide the Christmas she wants for her children because of a Conservative 'green' agenda... Number Ten needs to talk to the Sally Websters in Coronation Street as much as it does the modern-day Lady Mary in Notting Hill. As a working-class northerner, I can assure you that just about every woman north of the Watford Gap takes huge exception to both men and women with plummy accents and Savile Row suits dictating policy which affects their lives. It's a Northern thing. We don't trust people who talk posh and we are utterly repelled by arrogance."

Dorries also observed: "Women are good at revenge, a dish best served cold." David Cameron has just been served with double helpings – and there may be plenty more where that came from.