Under the plan, local authorities would fund places at private and state-run boarding schools for young people in children's homes and foster families. It is hoped that the initiative will provide a more stable background and better educational opportunities than the present system, which Tony Blair admitted last week was failing thousands of children.
A pilot scheme, due to be launched next year, will be discussed at a working group of government officials, local authorities, boarding schools and relevant charities this week.
Abberley Hall, in Worcester, and Oundle School, near Peterborough, are among about 50 preparatory and secondary schools that have so far shown interest in taking part, and, while the numbers of children involved initially will be very small, members of the Boarding Schools Association are prepared to offer the scheme up to 2,000 places.
Adrian Underwood, the director of the association, which represents about 500 boarding schools, including 35 state schools, said: "It is a long process and there is a lot of red tape but we are very interested in this. In the short term, we might only be talking about 50 or 60 children, but there are 500 boarding schools spread across the UK and I see no reason why they might not take an average of four children, which would make a considerable difference to the fate of looked-after children in this country."
Official figures show that only six per cent of the 60,000 children in care gain five or more A to C GCSEs and more than a third are not entered for a single GCSE.
Conviction rates for young people in care are three times the rate for other juveniles. One in four girls leaving care is pregnant or already a mother. A recent case which caused outrage involved a 12-year-old living in a children's home in Blackburn who became pregnant while working as a prostitute.
Dismal outcomes are the norm despite the £2.5 billion a year spent looking after them. It costs £100,000 a year to keep a child in a children's home, more than four times the fees at top private schools such as Eton or Winchester.
Fostering can cost up to £30,000 a year, compared with the £7,500 a year that state boarding schools charge parents for accommodation, with the £5,000 cost of education covered by the local authorities.
A report published recently by the Commission for Social Care Inspection revealed that 13 per cent of fostered children had experienced three or more placements in a year, often necessitating a change in school.
Behaviour problems are a common cause of the breakdown of foster arrangements, and a number of charities, including the National Children's Bureau, are sceptical about whether boarding schools can cope with disturbed children.
A spokesman said: "Most children in care are there because they have been abused and neglected. Will schools be ready to meet their emotional needs?"
Mr Underwood said that the scheme could not provide the answer for young people who were veering towards delinquency, not least because fee-paying parents would object. We would not have a hope with a 14-year-old who has been in a secure unit, for instance," he said. "The key is to look at which children would benefit from boarding school and who wants to go."
During holidays, children could stay with foster carers, return to their families or remain at school.
The scheme already has support from Lord Adonis, the former head of the Downing Street policy unit and now an education minister. He was raised by his father in a council flat in Camden and funded by charitable trusts to attend Kingham Hill independent boarding school, in the Cotswolds.
Further signs of the growing acceptance of boarding schools as a viable alternative to social care include plans for the first city academy to offer boarding places. Kingshurst City Technology College, in Birmingham, is planning to convert to an academy, sponsored by HSBC, with room for 100 boarders. A fifth of places would go to children in care.