The Wirral couple took legal action on their daughter's behalf after a clerk's mistake raised their hopes that she would receive exclusive and constant 'one-to-one assistance' while in school.
In fact, the authority had only agreed that experienced assistants be made 'available' to support the girl 'for every hour of every day that she is in school'.
In February this year Mr Justice Maurice Kay dismissed the parents' judicial review challenge, ruling that it would be 'absurd' for the council to be bound by a pure administrative error.
Lord Justice Potter said the court would give full reasons for its decision next month. (October)
'We are not in a position to give judgement now, but I can say that the appeal will be dismissed for reasons to be delivered later.'
The girl - who cannot be named - has suffered from severe athetoid cerebral palsy since birth, and has been the subject of successive statements of special educational needs since February 1994.
She attends a special school for children with complex learning difficulties, but her parents maintain she needs a full-time, one-to-one support assistant for every hour she is at school.
The most the council would offer was twelve and a half hours' support from a welfare assistant, a decision which triggered the parents' appeal to the Special Educational Needs Tribunal.
But agreement was reached before the hearing and the tribunal directed that an experienced assistant be made 'available' to support the girl throughout the day.
The dispute centred on the council's subsequent statement which, due to the clerk's error, failed to follow the same wording as the tribunal's order.
The family's counsel, Nicholas Bowen, argued that the council should be made to abide by the clerk's mistake.
But in his February decision, Mr Justice Maurice Kay said the mistake had been made 'in good faith' and it would be wrong to make the council do more for the girl than it had been directed to do by the tribunal.
Strand News Service