Red Toryism sounds like a paradox too far. Yet it has become the shorthand term for a new Tory think-tank. Although social justice sounds inextricably entwined with socialism, the Centre for Social Justice (CSJ) is another – and very effective – Tory think-tank run by Iain Duncan Smith. Does this mean that the Cameroons have repudiated Thatcherism? No, but they are moving beyond it. Thatcherism is not enough. It is time for a new Hegelian synthesis.

The Lady always had the defects of her qualities. When she said "there is no such thing as society" she was merely being scornful about defence-counsel weaselry: attempts to persuade the court that even if the defendant might have coshed an old dear while stealing her pension, it was all society's fault. But a more intellectually-sensitive Tory would have found another form of words.

It is not clear whether Margaret Thatcher is a Tory, as opposed to a classical liberal. She does not have a Tory temperament. Traditional Tories believe that religion requires faith: secular matters, scepticism. Lady Thatcher inverted that. She is a conviction politician but her religious views are tepid. Tories know that freedom is not a panacea and that the social order requires more than anarchy plus the constable. Much less persuaded by the ubiquity of original sin or by the connection between liberty and licence, Margaret Thatcher thought that people should be free to do what they ought to do, and that the constable would be able to deal with the minority who misbehaved.

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Above all, she believed that if you kept government out of the way and allowed people to run their own lives, most of them would be successful. She neither understood nor sympathised with those who could not succeed – because she thought that it was their own fault for not trying hard enough. Traditional Toryism is much more humane, much more attuned to human weakness and to the plight of those trapped at the bottom of the heap. As Mrs Thatcher was an electoral politician, she would never have said it, but she regarded all that as wet.

David Cameron would not agree. The proper name for the Red Tory think-tank is ResPublica. No, this does not mean that the Tories are no longer monarchists. Res publica means public things: a public agenda. Mr Cameron is committed to such an agenda. His approach to social policy is summarised in two sentences: "we are all in this together" and "there is such a thing as society but it is not the same as the state".

Two or three years ago, Mr Cameron talked a lot about the quality of life index and said that it was just important as the economic indices; in those days, it seemed as if the latter ones could be taken for granted. Of late, the Tory leader has had to adapt his rhetoric to a colder climate, but he is still determined to ensure that his party will not just sound like the political wing of the Treasury.

Like all sensible Tories, he is aware of the failures of welfarism: the danger that by trapping its clients in a dependency culture, welfare can perpetuate the cycle of deprivation, so that the welfare state becomes an ill-fare state. He is equally aware that the answer does not lie in benign neglect. Mr Cameron believes that welfare provision should be much less monolithic: that charities and voluntary organisations should be encouraged to involve themselves and help ensure that the enormous expenditures actually promote welfare.

If ResPublica and the CSJ can work out how to achieve this, they will find many doors open to them in David Cameron's Whitehall. The likelihood is that they will both have a considerable influence on policy, but that neither will be fully successful. That will not be their fault. Like everyone else in the field, they are pursuing an unattainable goal and confronted by an insuperable obstacle.

The unattainable goal is the Tories' dream: a country that combines the social harmony of the 1950s with the economic dynamism of recent decades: a fusion of the post-Big Bang City and Watch with Mother. In one respect, Marx had a clearer insight into capitalism than most Tories. He understood its destructive power. He knew that it would undermine traditional hierarchies and the social stability which they created. It is easy to argue that man was designed to live in a tribal, hierarchical, agrarian and religious world. In rending that world apart, capitalism has made it possible for billions of people to enjoy previously unimaginable levels of freedom, prosperity – and longevity. But there is a price. To paraphrase Freud, the outcome is often capitalism and its discontents.

Not everyone can cope with the relentless drive from status to contract: hence our insuperable obstacle, the underclass. Eric Hobsbawm wrote that the first generation of industrial workers often responded to their new circumstances with dreams and violence. The same is true of the first post-industrial generation. Since 1960, there has been a relentless decline in the family and in religion as a social cement. Over the same decades, television has ruthlessly sabotaged the satisfactions, the status and the self-respect that used to sustain the less well-off, by bombarding them with images of a consumer's paradise that they have no hope of enjoying, and that appears to have become the whole meaning of life.

Leftie sociologists who used to complain about the imposition of social control on the poor ought to be happier these days, when there is so much less of it about. In some inner cities, we now have anarchy without the constable.

It will take more than think-tanks to put that right. Phillip Blond, who runs ResPublica, is religious. He would like to promote a religious revival. It would be unwise to have much faith in the outcome. Yet even if it is not Divine, some form of intervention will be necessary. One possible solution, previously canvassed here, is a new cadre of social workers. Middle-aged housewives, those leaving the armed forces or the police, businessmen who have retired early and are up to a new challenge: give them all a case-load of underclass single mothers to turn into decent mothers who can bring up non-criminal children.

That might sound coercive, and it would have tough-love elements. It should also add to the sum of human happiness. It would train those who cannot cope with freedom how to enjoy all the rights which Mrs Thatcher believes that they ought to have. The Victorians did succeed in moralising an underclass: not the smallest of their achievements. We have to remoralise one. They had two resources which we lack: strong families and strong churches. But we spend vastly more money than they would have dreamt of. We must now secure value for that money.

JS Mill described the Tories as the stupid party (not that this upset many Tories). It was always untrue and never more so than under Margaret Thatcher, who delighted in winning intellectual converts. Although these distinguished figures made an insignificant contribution to electoral success, the sense that the Party was an idée en marche boosted Tory morale. There may have been fewer well-known names in recent years, but Tory think-tank culture has never been healthier: the ones mentioned above, Policy Exchange and several others. This is just as well. Rarely has every area of public policy been more embattled; rarely has hard thinking been more urgent. ResPublica will have to prove that it can turn phrases into policies. So will the Cameron government.