The accusations came last week in a report commissioned by the Independent Schools Joint Council. More than 200 fee-paying schools said they were discouraged when they proposed sharing facilities.

They blamed apathy or opposition on the part of local authorities, a charge denied by the Local Government Association.

The spat between leading figures in the state and independent sectors suggests that a Government advisory group set up to look at ways of making partnership work in practice still has much to do.

The group was established after an announcement in December when Stephen Byers, the standards minister, declared an end to “educational apartheid” and promised Pounds 300,000 for joint initiatives between state and private schools.

Graham Lane, chairman of the LGA’s education committee, said local authorities were willing partners and pointed out that they had entered into all sorts of partnerships with, among others, industry and training and enterprise councils.

Mr Lane said: “We are very interested in partnerships, but what is important is that it takes two to form a partnership. What is in it for the independent school? I don’t know of any LEA that has rejected any proposal.”

He added: “The private system is still sore about the end of the Assisted Places Scheme and this report is propaganda by them. If they want to open up their facilities, then come forward with plans.” What local authorities would not do, he stressed, is put cash into such schemes when there were more important calls on their money and the independent sector was already getting help through tax relief.

Jonathan Horsman, political liaison officer with the Independent Schools Information Service, strongly denied the survey was undertaken for propaganda reasons. He said he was delighted the LGA, representing LEAs, wanted to work in partnership with the private sector “even in those areas where there has been a problem in the past”.

He added: “The purpose of the survey was to find out what sort of co-operation exists between independent and state schools and identify examples of good practice. All along we have purposely not singled out a school or an LEA where problems have been experienced.”

The council commissioned the survey of 945 independent schools before the election, but the results will provide important evidence for the advisory group looking to encourage partnership between independent and state sectors.

The survey shows that three-quarters of independent schools are involved in joint activities with their communities or neighbouring state schools. Games and sport, community service and music predominate.

Ian Beer, ISC chairman and a former head of Harrow School, said the report demonstrated that partnership and co-operation were embedded in the independent ethos, but he acknowledged more could be done.

He said: “We hope schools in both sectors will be encouraged to new contacts by the range and variety of what is already being done. This is a challenge for both sectors.”