The rising costs have come despite the fact that local authorities are paying for fewer pupils to attend independent and non-maintained special schools than they did two years ago.

Since 2003 the number of these placements for young people aged up to 19 has dropped by 6 per cent but the average fees have risen by nearly a fifth to pound;49,570 per child.

The biggest increase in demand has been for residential care, costing local council taxpayers more than pound;200,000 per pupil each year. An estimated 161 children receive this support, often consisting of 24-hour supervision by two or more staff members, which is nearly five times as many as two years ago.

There are at least four pupils in England whose placements cost more than pound;500,000 a year each because of their extreme disabilities or behavioural problems.

The figures were revealed in an annual survey by the 11 SEN regional partnerships set up by the Government.

Hugh Clench, the survey’s co-ordinator and facilitator for the South Central Regional Inclusion Partnership, said it was hard to explain the price increase.

Children with grave medical problems are living longer and a growing proportion of places are needed for pupils with autism and behavioural, emotional and social difficulties, he said, which comprise half the placements and 60 per cent of the costs.

Another factor was that some private special schools had put their fees up to cope with increases in national insurance.

“The lion’s share of the placements were for secondary-age pupils which suggests that mainstream schools and maintained special schools are less able to cope with a wide range of special needs as children get older,” he said.

Mr Clench said that he did not support increasing numbers in maintained special schools. However, he said that greater inclusion would free up places in state special schools for pupils who were now being educated privately.

Another survey finding was that ethnic-minority pupils had disproportionately few private placements, even though some groups, such as black Caribbean pupils, are more likely to suffer emotional or behavioural difficulties.

Mr Clench said it was hard to explain the reason, though cultural differences were a possibility as middle-class white families could press hard for private treatment while anecdotal evidence suggested that Asian families could be unwilling to admit that their children needed special care.

The Commons education select committee and the Conservative party are carrying out separate investigations into special needs.

Barry Sheerman, Labour MP and chairman of the select committee, said MPs would be examining the cost of private care but that he understood why it could be expensive.

“The figures look astonishing but when you go to these schools you see children who can only communicate by tapping messages on a computer, and they need 24-hour care,” he said.

Tudor Lodge, a private special school in Purley, Surrey, which charges fees of more than pound;100,000 a year, was criticised by inspectors this year for providing pupils with trips to bowling alleys and cinemas rather than a structured timetable.

David Cameron, Conservative education spokesman, said: “It cannot be right that while the Government’s inclusion agenda is shutting state special schools, local authorities are having to spend more on private provision.”

A spokesman for the Department for Education and Skills said that residential care for pupils with complex needs was bound to be expensive but that children needed the support which was best for them.

FEFOCUS 2, friday magazine 6 Out of Authority Placements 2005 is at www.scrip.uk.net