Not because I disagreed with Ms Millar, whose thesis was that parental choice of schools is a damaging illusion. I have two quite different gripes. The first is that I, echoing the views of most people who work in schools, have been pointing out the pitfalls of parental choice for nearly 30 years. We have been dismissed as old Labour defenders of producer interests, and as enemies of rising standards. Nobody in power has paid the slightest attention. Yet Ms Millar, as the partner of Alastair Campbell, Tony Blair’s former press secretary, and a former adviser to Cherie Blair, was inside the magic Downing Street circle (where the need to enhance parental choice is taken as axiomatic) for nearly a decade.

To be fair, the couple’s robust views on comprehensives were never a secret in elite metropolitan circles. But those views were not known to most teachers in struggling schools, who suffered parental flight and an unstoppable spiral of decline as a result of Government policies on choice.

I do not complain that the couple failed to change official policy. But I think they could have tried to get a more polite hearing for those who disagreed with it.

My second gripe is that Ms Millar has missed the point. She believes that all parents should send their children to the local school. To me, this implies that the Government should compel them to do so. If not, Ms Millar is being absurdly optimistic, since I can think of few examples of the middle classes choosing to behave ethically. Global warming is supposed to be a fashionable concern, yet the middle classes increasingly travel in gas-guzzling four-wheel drives, often to convey their offspring to schools miles from their homes.

But as Phil Collins, director of the Social Market Foundation, pointed out in these pages last week, a policy favouring neighbourhood schools gets us nowhere. The prices that parents pay to get properties within the catchment areas of favoured schools would rise higher still. Instances of children being put out to “board” with long-lost aunts, would increase. Adopt a “local first” policy and you end up with yet more social segregation.

Let me spell out why we need socially mixed schools. It is not because of some sentimental idea of social cohesion but because the single most effective way of boosting a school’s achievement is not to give it better teachers, more inspections or even more money. It is to change the pupil intake, reducing the numbers from poor homes. If every school were socially mixed, “bad” schools as now understood would disappear and average pupil achievement would rise sharply.

One way of achieving this is to bus middle-class children to schools in poor areas, or vice versa. This would be denounced as social engineering and state dictatorship. I do not see that it is worse than middle-class parents busing their children across big cities so that they can attend the “best” schools. But I do not trust bureaucrats to organise it, and it is probably not practical politics.

I, therefore, turn to a solution, which I have also advocated as the answer to socially biased entry to Oxford and Cambridge. This is to allocate a fixed number of places at the elite Russell Group universities to each school in the country, proportionate to the number of pupils in the school.

This would transform the schools market, removing any incentives for middle-class parents to seek the “best” schools or for them to go private.

Instead, they would clamour for places in the most deprived inner-city neighbourhoods. What a pity that Ms Millar did not use her Channel 4 slot to propose something as revolutionary as that.

Peter Wilby is editor of the New Statesman