Mr Byers welcomed a survey showing that more than three-quarters of private schools have at least one joint activity with either the local community or state school.
But he said that the Government's initiative to foster partnership between state and private schools aimed to raise academic standards. "The survey shows that whilst there are many independent schools involved in community- based activities, the educational links between the independent and state sector are still very much in the early stages of development," he added.
The survey of 950 fee-paying schools from the Independent Schools Council found that six out of ten allowed community use of sports, music or drama facilities but only 17 per cent let state schools use the facilities even occasionally. The figure for frequent use was just 4 per cent.
When a similar survey was carried out five years ago, facilities were usually made available free of charge. A nominal or at cost charge is now more common. Charging for profit is rare. There were few examples of links between teachers and pupils and very few teacher exchanges.
The survey was commissioned before the general election, when Labour was questioning the charitable status of independent schools - worth around pounds 65m.
However, before Christmas Mr Byers called a halt to hostilities between Labour and independent schools when he announced pounds 500,000 for joint initiatives between state and private schools. A working group is examining how they should develop.
Ian Beer, former head of Harrow and the council's chairman, said partnership and co-operation were embedded in the independent school ethos. "This is not a glib response to a new political climate. The majority of partnerships and co-operative arrangements are very well established." But much more could be done, he said.
The report points out that a small number of local authorities continue to resist co-operation between private and state schools. More than 200 fee-paying schools said proposals to share facilities had been discouraged.
Only one school reported that parents were unenthusiastic about contact with state schools because they were worried about a "rough element".
Examples of co-operation outlined at the briefing on the survey included:
St Michael's, Leigh-on-Sea, Essex, a prep school which offers primary school pupils after-school language lessons.
Eton College, Berkshire which runs a summer school to help pupils from the London borough of Brent to bridge the gap between GCSE and A-level.
Latymer Upper/St Paul's Schools, London which have a Saturday school for primary pupils in maths, English, science and technology.
St James and the Abbey, West Malvern which runs student leadership courses and training programmes for state and independent school teachers.
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