As ministers have ratcheted up pressure in the last few weeks on major independent schools to forge closer links with the maintained sector, world-famous institutions including Harrow and St Paul's have revealed they are working on proposals to take over "failing" primaries.
The move is in response to the Primary School Academy Group, an initiative unveiled by the Headmasters' and Headmistresses' Conference (HMC) last month to encourage top public schools to sponsor underperforming - or "below-the-floor" - primary schools. Now TES can reveal that some of the very best known schools of this kind - including Harrow, St Paul's, Manchester Grammar and Dulwich College - are actively looking at the idea of setting up primary academies.
"We have got a number of schools that have expressed serious interest in sponsoring an academy," said David Levin, headmaster of City of London School and chair of the new HMC group.
These schools are now set to speak to Department for Education sponsor broker Felicity Gillespie, whose role at the department is to line up sponsor schools with failing primaries.
Mr Levin previously sent a letter to all HMC schools asking them to consider sponsoring a primary. But he went further last week. "There are a number of factors as to why we should invest. It is part of our duty as citizens of this country. We need to give back to society to enhance social mobility. Academies are going to be a permanent part of the landscape. All political parties are in unanimous approval of academies."
Mr Levin is considering personal sponsorship of a primary in south London because the governance structure of his own school makes it difficult for it to underake sponsorship. He hopes to have it in place by next September and said he hoped the involvement of independents would have the "blessing of local authorities".
"Independents could take over a below-the-floor school and make changes from within. They would bring in their own staff, which would make them attractive to primary school teachers, who otherwise might have been put off going there."
One school interested in sponsoring a primary academy is Harrow. Its new head, Jim Hawkins, said: "I understand the current Government's desire to get some of the public school DNA into the state sector. Sponsoring an academy or free school is one possibility, but the relationship won't be right if one side is feeling patronised. `Here we are, the wealthy school and we're coming to help' - that's never going to work."
The Independent Association of Prep Schools said it was close to announcing the name of its first member school to sponsor a primary.
The Government has increasingly been lobbying independents to get involved with underperforming state schools, and Mr Cameron told last week's Conservative party conference: "I want to see private schools start academies and sponsor academies in the state sector. The apartheid between our private and state schools is one of the biggest wasted opportunities in our country today."
The prime minister and Michael Gove recently held a summit with top independents on the subject, and HMC general secretary William Richardson admitted he expected to be asked for a progress report from the education secretary. But HMC chairman Ken Durham, who is also head of University College School in north London, warned the Government that independents should not be strong-armed into sponsoring academies. "If independent schools are to get involved in the state sector, it should be for education reasons. The idea that we should do it because somebody says we should, I don't go for that."
Free schools champion Toby Young, who is also hoping to persuade independents to set up free schools, said: "Privately, I've been approached by a number of (independent) headteachers about setting up free schools. But I don't think independents would respond well to compulsion. They would feel harried and bullied by the state."
But it is becoming clear that more and more independents will be expected to help struggling state schools - and increasingly, it seems, they see the best option is to take on primary schools.
Professor Robert Winston has attacked the founding in central London of the New College of the Humanities, a private university backed by philosopher AC Grayling.
The private college, which Professor Grayling said will be up and running next year, will charge students an annual fee of pound;18,000 but has said up to 30 per cent of the eventual 1,000 students will receive scholarships or assisted help - where the students pay the first pound;7,200 of the fees.
Professor Winston said he was not convinced Professor Grayling will be able to attract enough money to help bankroll the fees of poorer students.
"How is he going to get scholarships? A university has to be involved in research. Is he going to get researchers into there?
"I don't believe scientists want to work in his university. Places like Imperial, Oxford and Cambridge have got the track records and the international status."
Original headline: The top flight sets its sights on struggling primaries