Labour’s appeal for independents to share expertise and facilities with their less-favoured state cousins was a huge publicity boost for the private sector. The implied message is that all independent schools are superior to their state counterparts.

Many state schools would disagree. One Oxfordshire headteacher retorted that her school had more to offer its private-sector neighbours than they had to offer in return. “They couldn’t even offer me A-level Latin,” she added.

Yet let us not fall into “old prejudices”. Many independent schools provide excellent teaching. They can offer expertise such as preparing Oxbridge entrants. But the Government should have emphasised that it is a two-way process. The independents should not forget that the state pays for the training of most of their staff.

State schools have great expertise too, particularly when it comes to motivating the less able. Labour should beware the St Cake’s v. Bash Street Comprehensive stereotype. Some independent schools do have stunning facilities. Yet many large comprehensives have far better sports, technology, or music facilities than smaller, but expensive private schools. It is not always better just because you have to pay for it.

If this is about satisfying the Charity Commissioners, don’t let it become tokenism. The Government should not allow the independent sector to salve its collective conscience (and keep its tax perks) by playing Lady Bountiful to forelock-tugging state schools. Set them a higher goal: why not expect them to contribute a certain percentage of their fee income to partnerships with state schools?

The independent schools certainly know how to raise funds for themselves. Last year my household was plunged into the nightmare of secondary school transfer. Our area has excellent, but over-subscribed, state schools. There is no certainty of getting your first, second or even third choice. With some misgivings, we also applied to an independent.

Independents’ offers go out before state school places are decided. They ask for a deposit to secure the offer, payable before state school allocations are known. I was asked for Pounds 500. Unsure what other offers my daughter would receive, I paid.

When the state school offer came through some weeks later, I accepted it and kissed goodbye to Pounds 500. Later, when the state school asked new parents if they would mind paying a modest Pounds 25 a year into the school fund, I realised how easily independent schools take money from anxious parents.

Is it compatible with charitable status to require Pounds 500 from parents to reserve a place they may not take up? If the point is to stop parents holding several offers, how about passing on the deposit to the state (or private) school that will eventually bear the cost of educating the child?

There are, of course, some fine examples of independent schools helping state sector neighbours. Leeds High school sends girls to help at a local state primary. The primary school benefits. But so do the girls. It is good for their CVs and it will open their eyes.

The real test is whether independent schools will share something which has more than marginal costs. Will they let state schools use their music and sporting facilities on a regular basis during the school day? Will they lend their teacher of Russian or Greek to a state school, or will they simply invite one or two state school pupils to join their classes?

The demise of the Assisted Places Scheme will be one test of the charity of the independent sector. Some, like the Girls’ Schools Association, plan replacement scholarships. But, at very best, the independent sector might fund one-third of the number of current assisted places.

Yet this is the sort of charity the independent sector finds easiest, namely helping poor but very bright pupils. The children benefit, but so does the school. It boosts its examination success, which in turn attracts more fee-payers. Scholarships are the independent schools’ loss leaders.

So, while Labour is right to drop its old hostility to independent schools, it should ask for much more in return. When independent schools do much more to help children who are difficult, deprived or just plain average, then they will have earned their charitable status.

Mike Baker is the BBC’s education correspondent