Private schools have offered to create 10,000 free places for poorer students, but only if the Government helps fund them.
The move comes after Prime Minister Theresa May warned in a Green Paper that private schools would have to do more for society if they want to keep the tax privileges that come with their charitable status.
The proposal, by the Independent Schools Council, suggests the Government pays no more than the cost of a state school place per pupil, thought to be around £5,500 a year, with the private sector paying the rest.
It says places would be available to students of all ages, from prep school to sixth form.
Some children would be tested for ability, but the council said it was not aiming the places at top academy or grammar school pupils, but families on lower incomes.
Its chairman Barnaby Lenon said: “The proposals we are putting forward go considerably further than some of the ideas the Green Paper suggested and, by helping create more good school places, both in state and independent schools, we would be helping to expand real social mobility in this country.”
But outgoing Chief Inspector of Schools Sir Michael Wilshaw said the proposals did not go far enough.
He said: “I think they can do better than that and if I was Government I would be asking them to do more as a quid pro quo for their tax privileges.”
There are around 2,500 independent schools in Britain, with a combined attendance of about 615,000 children. Their charitable status means, amongst other benefits, that they are not charged business rates by local councils.
Baroness Estelle Morris, an ex-teacher and former Education Secretary in the last Labour government, said: “This is about a request to use state money, taxpayers’ money, to extract the brightest children out of our comprehensive schools and skim then off and put them into public schools, and that’s not good for the education system.”
Critics have long questioned the charitable status of private schools because most pupils come from wealthy families.
Mike Buchanan, chairman of the Headmasters’ and Headmistresses’ Conference, an association of heads of leading independent schools, said: “This innovative plan could herald a new era of co-operation between Government and independent schools to offer outstanding education to a new generation of children from lower income homes.
“Offering jointly-funded places in independent schools is a high-impact, low-risk idea which will be zero additional cost to the taxpayer.
“Those schools already give free and partly-funded places to thousands of children to try and offer them the best possible start. We want to do more, and hope the Government will put pupils before politics.”
The proposal was announced on the same day a report by the Sutton Trust revealed that children judged to be from “just about managing” families were “significantly” less likely to attend a grammar school than their wealthier counterparts.
A Department for Education spokesman said: “Our proposals are about creating more choice, with more good school places for more parents in more parts of the country. “We want to do this by lifting the ban on new grammars, and harnessing the resources and expertise of universities, faith schools and independent schools.”