Forcing private schools to work with their neighbours in the state sector would result in their relationships being "tarnished", a leading figure in the independent sector has warned.
Tristram Hunt's insistence that private schools should be forced to break down the "corrosive divide of privilege" by working with state schools came in for fierce criticism from the independent sector last year.
Now the chair of the Independent Schools Council (ISC) has insisted that many independent schools "don't have much money", and would need government funding if they were to reach out to support their neighbours in the state sector.
"Encouragement is a good idea, and some government funding is frankly quite a good idea because it all costs money and a lot of independent schools don't have much," Barnaby Lenon, former headmaster of Harrow School, told TES.
"The notion that independent schools have lots of staff sitting around with long enough to go off and teach at other schools, and that they've got lots of money sitting around which can fund all these things, is just, of course, a myth."
Mr Lenon said fee-paying schools should not be "forced" into partnerships with the state sector.
"My own view as someone who was a headmaster for many years and did independent-state school partnerships on a big scale, is that being told to do things by the Charity Commission or by the government is not the most effective way of persuading people to work together.
"If you're going to work together you want to do so with a sense of energy and moral purpose, which stems from an understanding of the mutual benefit of these partnerships. If you're being forced to do it.it gets tarnished," he said.
Mr Lenon said independent schools had continued to increase the amount they spent on bursaries since 2011, when a landmark High Court ruling said that private schools, which have charitable status, must provide more than a "token" benefit to the less well-off.
Mr Lenon said one of the ISC's top priorities was to remedy what it saw as public misconceptions about independent schools. "We're trying to get away from the perception that all our parents are rich, because actually most of our schools are serving their local community and providing children with the opportunities their parents want," he said.
"In big cities such as London and Birmingham, schools are providing a marvellous academic education for the local community with vast numbers of bursaries, so that income is not the barrier it might once have been. Many of our schools are quite small."
Mr Lenon also called for a "period of stability" following wide-ranging reforms to exams and the curriculum. "Teachers have been working very hard preparing for these reformed qualifications," he said. "It would be nice to see their work rewarded with at least five years where the syllabus was stable."
Read more in Funding for Independent Schools, free this week