All week during our family holiday we wondered what might have happened to the father. Our children played with theirs, and we chatted to the mother. Had there been a separation, or worse a tragedy, we idly wondered? Only on the last night did the mother, a high-powered barrister, explain that her husband was at board meetings in Dubai. She spoke of their children’s schools: “We are so thrilled that they are all at grammar schools: we think it is so much better for them morally.”

I had heard this before, and it troubled me. Stories are increasingly appearing of middle-class parents buying their way into the catchment areas of desirable state schools, discovering religion and in other ways manipulating their children into choice state schools. When such parents boasted of a moral superiority over parents who paid fees, it seemed even more wrong to me. At the time I was running Brighton college, and almost daily I was encountering parents who were finding it hard to pay. Like parents who used the sector everywhere, they were making financial sacrifices, forgoing holidays and cars, dipping into their savings and asking their own parents to help. Were such actions really worthy of moral opprobrium?

The evidence has mounted of the middle classes dominating places at the top state schools. The Sutton Trust in 2005 found that the top 200 secondary state schools were disproportionately patronised by the better-off. It found that only 3% of children at these schools were eligible for free school meals, compared with 12.3% in their local areas and 14.3% nationally. Research this month by Rebecca Allen from the Institute of Education showed a similar dominance at faith schools by children from better-off backgrounds. Top sixth-form colleges, such as Hills Road in Cambridge, are also packed with middle-class children.

It is clear that the present system of a fee-paying sector and a non-fee-paying sector is morally impossible to defend. The powerful and articulate will always find ways to manipulate a free system. There is nothing intrinsically wrong in this: they are doing what all parents would do – getting the best for their children. It is the system that is wrong.

Yet the system can change. I believe that the state should charge fees for the well-off. Unpopular schools should be free to those of little means, and charge low fees to the well-off, of say £1,000 a year. Highly popular state schools should still be free to poorer families, but should be open to others on a sliding scale according to parental wealth up to a maximum figure of say £8,000 per year, possibly with tax breaks.

Already countries abroad are adopting such a system. In Hong Kong, state schools apply to the government for the right to be able to charge fees. A new booklet last month from Policy Exchange, Helping Schools Succeed, cites state school head teachers arguing that “what is free is not valued” and that free education is not providing the incentive for parents to expect high standards.

An independent commission should be set up immediately to examine this question. Fee paying by the well-off is not only morally but socially just, and would dramatically improve the schools and opportunities for all.

Anthony Seldon is master of Wellington college

Times Recommends

• Charles blazes trail as sun king
• Thalidomiders win payout 50 years on
• Libel gag on talk of 'medical hurricane'