The meritocratic ideal has a powerful grip on contemporary politicians. It seems deeply unfair that some people have fewer opportunities to reap the unequally distributed rewards of our society simply because they are born into households that are themselves impoverished.

In a truly meritocratic society, a citizen’s social class of origin should have no impact on their chances for success. Yet very few societies have come anywhere close to this ideal. In Britain, for example, although the proportion of working-class children attending university has steadily increased over the past 50 years, this has only been in line with the increase in the proportion of 18-year-olds attending university.

Relatively, it is as great an advantage to be born well in 2003 as it was in 1953.

Estelle Morris, the former education secretary, frequently stated her ambition to eliminate the connection between social class and educational success. But any efforts to achieve this through education policy face two serious problems. First, it is very hard to compensate for disadvantage through education: it is easier and more effective to eliminate disadvantage at its source. Second, such efforts involve targeting resources at the least advantaged. But targeting the least advantaged in state schools runs the risk that wealthy parents will feel they are getting a bad deal - and defect to the private sector. This would be undesirable as the involvement of more advantaged parents and children in the state system is generally thought to benefit the least advantaged.

There are a number of reasons for this. First, lower-achieving children benefit from being taught alongside higher achievers. In addition, as schools come increasingly to rely on fundraising to top up their own resources, they gain from having parents who are more capable of raising (and donating) funds. And, crucially, if the most stimulating students are creamed off into the private sector, that sector becomes correspondingly more attractive to the best teachers.

For the policy-maker concerned with social mobility, therefore, the trick is to design policies which simultaneously target the least advantaged and lower-achieving children, while reassuring the middle-class parent. The first part of this equation is relatively straightforward. First, alter the funding formula that determines school budget levels so that all children eligible for free school meals bring with them three times the normal amount of per-pupil funding. This helps to counteract the tendency of schools to prefer middle-class to less advantaged children and ensures that if low-income children do still concentrate in particular schools, they are at least better resourced.

Second, alter the structure of Fresh Start schools so that they have, for the first three years, guaranteed class sizes of no more than 15, rising to 22 over the next four years, so that smaller class sizes benefit the least advantaged, and have some real impact.

If Fresh Start schools were to have those kinds of guarantees, they might well attract parents whose other choices are very expensive private schools or under-resourced state schools. If low-income children were to bring a lot of resources with them, the classrooms they inhabit would be better able to provide a decent learning atmosphere for all.

For those parents who are seeking unfair advantages for their children, or who cannot bear to have their children mix with the lower orders, these measures will do nothing. But for the large number of parents who simply want an adequately good school for their child, they might do quite a lot.

Professor Stephen Ball’s book Class Strategies and the Education Market (Routledge Falmer 2002) suggests that most parents considering whether or not to “go private” are, indeed, motivated mainly by the concern to ensure that their own child goes to an adequate school. Even some who do decide to go private bemoan the fact that there is not a school with a representative socio-economic mix available to their child.

And there is no evidence that increasing numbers of parents are fleeing the state system. The Institute for Public Policy Research’s Schooling in London shows that in the capital, despite increasing prosperity, especially among the wealthy, the percentage of children attending private schools has barely changed in the past two decades.

So the policy-maker’s dilemma might be less demanding than it seemed.

Still, it is worth remembering that we know comparatively little about how schooling can be used to counteract disadvantage, and do not have many examples of it doing so. Social mobility is easier to achieve through policies which simply eliminate social disadvantage - high employment and steeply progressive taxation. These policies simultaneously make social mobility less important, by equalising people’s life chances and lowering the stakes in the lottery of birth.

Harry Brighouse is professor of the philosophy of education at London University’s Institute of Education