Like all new Labour policies, the proposal for 200 city academies can be presented in different ways to different audiences. Labour backbenchers can be told that deprived areas will get expensive, gleaming new schools that will benefit children from poor families. With luck, Daily Mail readers will think they are re-born grammar schools. Business people will be impressed by the invitation to act as co-sponsors of the new schools, while knowing perfectly well that they won’t be required to put in significant amounts of real money.

But the main selling point of the city academies - and the one that appeals most to 10 Downing Street - is that they will persuade middle-class parents to stay in the state sector. The big challenge for public services, runs the Blairite argument, is to keep the middle-classes on board. If too many go private in education and health, their resistance to paying taxes for state schools and hospitals will grow. The answer is to offer them many of the things they would get in the private sector: choice, uniform, the house system - and yes, a degree of exclusivity if not outright selection. Even if the middle-classes grab places in the best state schools and their children get a disproportionate share of the resources, pupils in less favoured schools will benefit from a sort of trickle-down effect - because the pot of money available will be larger than it would otherwise be.

Ministers do not put it quite like that, but that is their drift.

It ought to be obvious that this aspiration to attract the middle-classes could conflict with the aspiration to help children in deprived areas. But I will leave that to one side and challenge Number 10‘s position more fundamentally. I do not accept that the “flight” to the fee-charging sector is a response to “failure” in the state sector. The section of the population that was traditionally willing to pay for education - the affluent middle-class - has grown exponentially in the past 40 years. A growth in school fee-paying is no more surprising than the growth in private sports centre subscriptions or holidays in Tuscany. Moreover, thousands are now willing to pay fees for daughters, where once they would have paid only for sons.

Fees have soared above inflation, but they are within the reach of more parents, not only because of higher incomes but because of smaller families and a growth in day schooling as opposed to boarding. State schools have done well to hold on to 93 per cent of the child population.

I see no clear correlation between the proportion of children attending fee-charging schools in particular areas and the condition of the local state schools. True, 14 per cent of inner London’s children are educated privately, but inner London contains high numbers of affluent parents. Look at the breakdown by borough and you will see that, for example, Richmond and Camden, which are thought to have “good” state schools, have more than 25 per cent of their children in the private sector. Islington and Waltham Forest, criticised for various sorts of “failure”, have fewer than 6 per cent.

For most parents, sending children to fee-charging schools is a choice dictated by lifestyle and status aspirations, like the decision to buy a four-wheel-drive for use in towns. Only members of the Prime Minister’s circle of metropolitan liberals feel embarrassed about paying fees and would definitely prefer “good” (for which read “exclusive”) state schools.

It is just possible that city academies will acquire the social cachet that the middle-classes crave. If so, and if half their pupils came from families that would otherwise pay, they would cut numbers in the fee-charging sector by more than 20 per cent. But pound;6.2 billion (I extrapolate from the cost of the pioneer academy in Bexley) seems a vast sum to spend on what is no more than a hunch.

Peter Wilby is editor of the New Statesman