Michael Mavor, chairman of the Headmasters’ and Headmistresses’ Conference suggested the idea, but it has been rejected by the second largest teachers’ union. The NASUWT said that independent schools could not offer trainees “adequate preparation” for state schools.

And one independent school currently involved in school-based training warned that running a scheme could be very time-consuming.

School-based initial teacher training was set up by the last government as a more practical alternative to conventional postgraduate or college courses. Schemes are run through a group of schools, with one managing the project.

Academic courses in subjects such as the history or philosophy of education are bought in from universities.

So far only a few independent schools have taken part and none has yet played a leading role.

Mr Mavor, head of Rugby School, hopes to change this. He wants his school to administer a programme of initial training. Students would be able to do teaching practice there and at neighbouring state schools.

He called on other independent schools to try this approach when he spoke to the HMC annual conference in Brighton earlier this month.

Eamonn O’Kane, deputy general secretary of the NASUWT, said: “I wonder how relevant this sort of training would be. Teachers training in independent schools would not come across persistent behaviour problems or the effects of children living in deprived areas.

“Students could get a very distorted view of teaching and they would not be adequately prepared for the state sector.”

He said that the scheme reflected the nervousness of much of the independent sector towards the Labour Government.

Bernard Trafford, headteacher of Wolverhampton grammar, said he had a great deal of respect for Mr Mavor, but warned that the amount schools were able to do would depend on their size and resources.

Wolverhampton grammar was part of a SCITTscheme run by Thomas Telford city technology college. It has taken four Postgraduate Certificate in Education students for six months each.

He said: “We feel we give students a good grounding with pupils being motivated and with a busy extra-curricular life. It is tough and rewarding. We wanted to get involved for the overall good of the profession and the students bring fresh ideas.

“Running a project is a nice idea, but schools are here to teach children, not to train teachers, and I wonder whether we should distract ourselves from our core activity.”

Kevin Satchwell, headteacher of Thomas Telford, said his CTC planned to give up running the training scheme.

The college has taken the lead role for four years. This has meant co-ordinating the work of 15 schools, some of which are run by local authorities and some of which are grant-maintained or independent.

One member of staff at Thomas Telford works entirely on administering the scheme and the school does not make a profit from its work.

Mr Satchwell hopes to get one of the universities involved to take over the administration. A spokeswoman for the Teacher Training Agency said it welcomed applications to run school-based training.