But Michael Mavor, chairman of the leading group of independent schools, said the Government must meet them half way. Income tax and fees meant that parents paid twice for their children's education and "would be very wary if high standards of independent schools slipped as a result of too much diversification".
Mr Mavor, speaking at the annual meeting of the Headmasters' and Headmistresses' Conference in Brighton, said a balancing act was needed with schools showing good will and spending some money with the rest coming from local education authorities.
He hoped that the charitable status of the independent sector would not be used as a "bargaining bludgeon" by the Government.
He was pleased that the Government seemed well disposed to independent schools and it was clear that it valued their high standards.
"Of course we want to make our facilities and expertise available wherever possible, but while we can farsightedly help to plant trees and look after them, somebody has to pay for them otherwise our very high standards, exactly those standards for which the Government aches, will suffer."
Mr Mavor, head of Rugby School, said schools were already co-operating, mainly in sports, music and the arts. Dulwich College in south London and King Edward's in Birmingham had run literacy schemes last summer.
He hoped many schools would get involved with initial teacher training to combat the "frightening scarcity of teachers".
State sixth-formers could take minority interest subjects, such as Latin or Greek, at independent schools at the same cost to an education authority, he said.
Heads also indicated that they would like an end to GCSE exams and would not "go to the stake" for the present A-level system.
John Moore, head of King's School Worcester, who chairs the HMC academic policy committee, said there was no need for an exam at 16. Independent heads wanted age-related qualifications abolished. "I cannot see why we should go on indefinitely with a major hurdle at 16 coinciding with the school-leaving age and sending the wrong signals, which I believe no other major European country feels it necessary to send."
GCSEs were not a good preparation for A-levels as the switch from nine or 10 subjects to two or three was a nasty shock with pupils often making the wrong choices, said Dr Moore.
Mr Mavor said he wanted sixth-formers to take five A-levels. "It is right that all boys and girls stay in education until the age of 18 or 19. I suspect that the stars of GCSE and even of our present A-levels will have faded with the end of the first Labour administration."
Dr Moore said GCSEs could be replaced by records of attainment which would demonstrate the breadth of a pupil's education. This could be done without a massive and expensive range of exams. "It was time for a radical idea of going back to trusting teachers."
* Following a much-publicised spat between two rival schools on the cricket field early last summer, heads are considering a code of conduct to stamp out indiscipline and gamesmanship.
The code was drawn up by Chris Hurst, head of Sedbergh School in Cumbria, who said all schools had a responsibility to channel competitive instincts into fair play. Parents would also be included in the code as there was an increasing trend for adult spectators to become aggressive and use bad language.
* The Princess Royal warned that the drive to raise education standards might place excessive emphasis on information technology.
The first member of the Royal family to address an HMC conference, she said children were in danger of becoming isolated, communicating only through computers. The ability to teach people to interact with each other would be more of a challenge to teachers. Successful schools worked hard at linking academic and social skills.
"Computers are slaves - you need to know what you want them to do," she said.