If elected to office, Mr Blair will of course have indisputable manifesto authority for phasing out assisted places. But that essentially negative commitment hardly amounts to a strategy. It is certainly marginal to Labour’s historic position (never formally rescinded because still passionately held by many party supporters): that independent schools should be abolished or, at the very least, have their charitable status removed. Since both options, legally and politically, are very dubious runners in any case, does that mean that all New Labour can realistically do is adopt a stance which is, in essence, old Tory? Is there no alternative but to leave the independent sector market alone, but hope, unlike the Conservatives, that it may contract or even collapse because consumers stop choosing it? Suppose they never do? If that is the political reality, however inconvenient, then Mr Blair needs to tackle its implications.

The question then becomes: what role does he see the independent sector playing? A politically embarrassing offshore island, which may sink beneath a rising tide of improved public sector provision, but almost certainly won’t and is therefore best ignored? Or a significant contributor to raising standards, a partner rather than competitor in achieving his top priority?

But suppose that, bucking all the odds, a Conservative government has been returned or is re-elected next time round. The question is just as problematic for the Tories in the long term. Expanding the Assisted Places Scheme does not rebut the proposition, put as its starkest (oddly enough) by former Tory MP George Walden: that “as long as our independent sector remains divorced from the national educational enterprise, our state system is condemned to overall mediocrity”. Is the only Conservative answer to that trenchant challenge effectively to ignore it? Provided they get past the independent sector’s immigration controls, should those who wish to leave the state education mainland but can’t afford the fare have it paid for them from public funds? Does that go any way to meet Walden’s serious point? Hardly.

Strangely enough, New Labour’s re-thought approach to the relationship between public and private sector finance may point to a more positive strategy for both parties. When all the campaign shouting has died down, there is cross-party consensus that the marriage of public and private sector finance in state enterprise is here to stay. Pressed on last Sunday’s Breakfast with Frost, Blair made no bones about it. A Labour government would not seek to recreate a nationally owned rail service or halt the sale of MOD accommodation. Blair went further. In judging whether public and private investment should be yoked, the key considerations, Blair said, are what works and what is in the public interest.

The same criteria are worth applying to one of the largest national enterprises, education. For schools, the Conservatives’ uneasy answer has been to increase the public money subsidy to privately-funded schools through assisted places, even where that means more money to already rich charitable foundations. That marriage cannot annul the divorce which rightly worries Walden.

There could be a strong argument for a mirror-image strategy: for investigating how the wealthier parts of the independent sector could support a state system strapped for cash. It may be neither possible nor desirable to remove charitable status from independent schools. That does not mean that the Government should do nothing about those independent schools which may now be operating far from their original founders’ intentions .

Both major parties are committed to developing Private Finance Initiatives. What would be wrong with wealthy educational charities providing the finance? A Department for Education and Employment official told me last week that he had never been asked the question. He should have been, and Eton College may be wise to ask it before someone else does. And what about franchising? Radical policies are possible only if you abandon the doctrinaire.

Peter Smith is general secretary of the Association of Teachers and Lecturers