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 contemporary 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 middle-class parents 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 receive 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 potentially conflicts with the aspiration to help children in deprived areas. But I will leave that on one side and challenge the Downing Street position more fundamentally. I do not accept that the "flight" to the fee-charging sector is a response to "failure" in the state sector. First, the section of the population that was traditionally willing to pay for education - the affluent middle-class - has grown exponentially over 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.
Though fees have soared above inflation, they are within the reach of many more parents, not only because of higher incomes but also 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.
Second, 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, which are criticised for various sorts of "failure", have less 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 purchase 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 they did, and if half their pupils came from families who would otherwise pay, they would reduce numbers in the fee-charging sector by more than 20 per cent. But pound;6.2 billion (I am extrapolating from the cost of the pioneer academy in Bexley) seems a vast sum of money to spend on what is no more than a hunch.
Peter Wilby is editor of the New Statesman