The most famous image of David Cameron on a council estate was taken during a visit to Wythenshawe, Manchester in 2007. He ambles towards the camera in dark jacket, gleaming white shirt, no tie; all modern Conservative casual. A few paces behind, a hooded youth, fingers and thumb in the shape of a gun, mimes the assassination of the leader of the opposition.

The image dramatised the limits of Cameron’s plan to recast his party as agents of social reform. The new Tory leader had strayed from his natural habitat and met vigilante PR justice.

Cameron’s elite upbringing is not the liability that some class warriors of the left would like it to be, but it is still a sensitive topic in Downing Street. Last summer, the No 10 policy unit became interested in a report by the Policy Exchange thinktank, calling for urgent measures to redeem Britain’s most deprived estates. A speech was drafted for the prime minister. Then the whole thing was abruptly canned. Liberal Tory insiders believe that Cameron was persuaded by advisers, armed with opinion polls, that headlines about “sink estates” would only sharpen awareness of his rarefied background. There would be no votes in it.

Lynton Crosby, Cameron’s hired-gun strategist, demands silence on issues that draw attention to his client’s weaknesses. His technique is to broadcast strengths with such relentless monomania that the other side can’t get a word in, let alone change the subject. Photocalls on building sites, symbolising economic growth, are allowed. Scenes of urban deprivation are not.

Issues that excite the core Tory vote, but distract from the campaign message, are shut down with concessions. That is why Cameron is suddenly enthusiastic about grammar schools, declaring his support for plans to build a new one in Sevenoaks – or, technically speaking, a satellite of an old one in Tonbridge, six miles away. The law allows existing grammars to expand. They are not supposed to appear from scratch. The Kentish case probes that legal boundary.

Permission depends on education secretary Nicky Morgan, whose instructions, when appointed to replace Michael Gove, were to avoid all controversy. She would surely rather defer a decision, but the right of her party, spurred on by Ukip, is revisiting an old passion for the 11-plus and wants prompt satisfaction. It is a fixation that Cameron once described as “splashing around in the shallow end of educational debate” with “outdated mantras” unsuitable for government.

Attachment to grammars testifies to the power of nostalgia over evidence

Attachment to grammars testifies to the power of nostalgia over evidence. In the romantic telling, they are vintage motors of social mobility, giving children from modest backgrounds the kind of education that would otherwise only have been available at private schools. They germinated the potential of great politicians and playwrights.

But for every Alan Bennett or Margaret Thatcher there were scores of equally talented kids who slipped up on test day and sank in secondary moderns. Since wealth disparities show up in different children’s educational performance by the age of seven, the 11-plus isn’t an academic selection at all. It measures the financial resources of parents who can prep their kids for the exam with private tuition. That is a rational choice for them, but a bad system if it bestows big educational favours on the already favoured.

Some Tories understand this. David Willetts spelled it out in a speech in 2007, provoking fury on the back benches and giving Cameron an early taste for tactical surrender. Willetts was shuffled out of his education brief six weeks later.

The difficulty many Tories have grasping the case against grammar schools describes a wider problem the party has with the way the politics of social advancement have changed; specifically, the way wealth gaps alter the equation. The Conservative instinct to cherish individual enterprise is healthy. But the expression of that impulse as suspicion of all state meddling leads to denial of the hurdles some children face in fulfilling their dreams. The will to get on is an important ingredient in success, but even in heroic doses it can’t always overcome poverty. It is hard to do your homework if there is nowhere quiet to go, no computer in the house and the library has closed.

Labour has the opposite problem, tending to see all social malaise as a product of skewed income distribution. The instinct is then to treat it with injections of cash from the collective pot, which must grow as needs demand. That leaves some on the left baffled and hostile when people who have climbed the ladder by feats of personal gumption resent the taxman confiscating fruits of their toil. Addressing that blind spot was a vital component of the New Labour project that the party would be unwise to forget.

But just as foolish is Tories supposing they have a monopoly on “aspiration”, not seeing how worthless a coinage that is without restless action to spread opportunity. Complacency on that front (and not the haughty manner of Eton) is the kernel of Cameron’s failure to cleanse his party of its image as a favour bank for the rich. Nor is that neglect a symptom of rightward drift or insufficient “modernisation”. Thatcher understood that government sometimes has to smash established privilege if the ambitions of new generations are to be met.

Cameron still hopes to rekindle a Thatcherite flame. That is what lies behind policies, such as Help to Buy, that subsidise mortgages for first-time buyers, and the latest promise to build 200,000 budget houses. The plan is to rehabilitate Tory-voting as the natural creed of the self-starter, whose industry is rewarded with home-ownership. It is homage to the spirit of Thatcher’s Right to Buy that let council tenants kickstart a new middle-class life for themselves.

But as with grammar schools, it is policy by nostalgia, wishing the old ways to spread opportunity can be polished up as new. What do the Tories offer families for whom buying a house feels as financially remote as paying private tutors? Obstacles to social advancement change with time. Supporting aspiration in 2015 means something different to what it meant in 1979, 1997 or 2010. That is the lesson Cameron should have learned from his visit to that Manchester estate.