But they have been warned by Douglas Sinclair, the Convention of Scottish Local Authorities chief executive, to sort it out quickly. “Councils fighting with each other is not good for the image of local government in Scotland,’’ he told Cosla’s education and cultural services forum last week.

Leaders failed to agree a formula for inter-authority payments following a similar failure in February to end the two-year old dispute. Some councils claim others are profiteering by charging well above the actual costs.

Keir Bloomer, Clackmannan’s director of education, said an indirect consequence was the speeding up of services as councils were reluctant to pay over the odds for provision in another authority.

Clackmannan has taken neighbouring Falkirk to the Scottish Secretary after complaining about charges for pupils at Dawson Park School. Edinburgh is also in conflict with East Lothian.

Brian Oldrey, of Renfrewshire, complained his authority was being forced by Glasgow to pay twice for staffing. “We’re looking for equity in how we provide for children with special educational needs. Perhaps we should go back to the drawing board,’’ he suggested.

Elaine Murray, Cosla convener, said authorities did not have much confidence in officials’ figures on which the banding formula is based. Officials replied that the figures were based on Scottish Office information supplied by councils.

A sliding scale of charges begins at pound;8,000, although some councils say the true costs are only pound;6,500 for placements in day provision. Councils have agreed a fee of up to 5 per cent in administration.

A working group is being set up to resolve the saga.