The other day I found a balloon with a postcard attached in English, French and German, giving a child’s name and saying it came from a nearby private school. I was invited to post it back, with details of where I had found it. I would receive the refunded postage, plus an unspecified reward, if it proved to be the furthest-travelled balloon.

Since the balloon seemed unlikely to win, I suppose I could have ignored it. But I posted it stampless, hoping the Royal Mail would charge the school for delivering it. Thus, I said to myself, I would strike a small blow in the class war.

This was a silly, petty gesture. But the British education system drives one to such lengths. We not only have schools divided along class lines.

Worse, the success of the private sectors - based on far greater resources and on pupil selections - is used as a stick to beat the state sector. The praise for “good schools” in the private sector is as infuriating as the praise for the “brilliance” of coalition forces in Iraq.

When the black teenager Ryan Bell was plucked from poverty and underachievement by a television company and sent to the independent Catholic college Downside, his initial success was hailed as a private-sector triumph. When he was expelled for leading his classmates to drink, no one seemed to notice Downside’s lamentable failure. If it cannot cope with one teenager from a disadvantaged background, how superior is it?

As the political philosopher Adam Swift explained in his recent How Not to be a Hypocrite, the case for abolishing private schools is overwhelming, on grounds of national efficiency as well as social justice.

The fee-charging sector, by “creaming off” the most able pupils with the most supportive parents, makes state schools, which most children attend, significantly worse than they would be otherwise.

Swift is almost alone in making this argument; even the proposal that private schools should lose charitable status is rarely heard nowadays.

But, as the response to Swift’s book shows, the opposing camp has no inhibitions. Both Anthony Seldon, head of the private Brighton College (writing in Prospect magazine), and Alan Ryan, warden of New College, Oxford (writing in The Times Literary Supplement), accept that the unequal competition between state and private is bad for the country. Their answer is to abolish the state sector.

All schools would become independent and charge fees. But only the most affluent parents would pay entirely from their own pockets; the state would remit all, or part of, the fees to poorer families. The system would work rather as university fees work and would bring more money into schooling generally just as means-tested fees have brought more money into universities generally.

The proposal has a superficial attraction to sections of the left; Ryan’s passing mention of Ivan Illich makes it sound like liberationist deschooling. And if all schools were required to charge the same fees - and to use a lottery to select when they had a surplus of applicants - I might support it, too. But that is not what Seldon, at any rate, has in mind. He wants the likes of Brighton College to continue selecting the brightest pupils while pulling in state subsidies.

Do not ignore these proposals. New Labour may have improved standards in state education, but it has failed to close the gap with the private sectors - a variant of the SeldonRyan idea could tempt a future Tory government.

Peter Wilby is editor of the New Statesman.