The decision has for the first time established that LEAs have a common law "duty of care" to their pupils in the way that hospitals and health authorities have a duty of care to their patients.
It opens the way to former pupils from Hampshire, Dorset and Bromley to seek thousands of pounds in damages from the authorities which they claim failed to cater for their special educational needs.
Mark Christmas, now 20, wants to sue Hampshire County Council for ignoring his dyslexia, which he says damaged his education and future job prospects; a 16- year-old known as E claims that Dorset did not provide for his dyslexia and gave his parents negligent advice; while Richard Keating, aged 24 from Bromley, who spent six years out of school and has no qualifications as a result, argues that the authority failed to provide any reasonable education.
Mr Keating also claims that LEAs should be liable to pay twice over: not only for common-law negligence, but also for failing to carry out their statutory duties in relation to special needs. The five Law Lords rejected this.
They also dismissed two associated claims that council social services departments could be sued if they make damaging mistakes when placing children at risk of abuse in care. Lord Browne-Wilkinson said that allowing the cases to proceed would "cut across the whole statutory system set up for the protection of children at risk".
The education judgment, which upheld an earlier decision by the Court of Appeal, has provoked sharply divided reactions. It has delighted special needs advocates but left local authorities fearful of massively increased legal action.
"This is a major advance in the provision of education for vulnerable children," said solicitor Jack Rabinowicz, who represents Mr Keating. "LEAs will now be accountable when things go wrong. This should mean that authorities, schools and others are much more careful in dealing with children. I think its implications will go beyond special needs."
Robert Love, the solicitor for E in Dorset, said the decision would affect all teachers acting as "diagnostic experts" - any teacher responsible for determining a child's special educational needs.
The result would, he said, release an enormous backlog of cases. Mr Love alone has around 30 people on his books anxious to seek damages. Back in 1992 the Queen's Bench Division of the High Court warned that allowing parents to sue education authorities could "open the floodgates".
Stephen Grosz, solicitor for Mark Christmas, said: "Broadly, if a pupil is underachieving teachers have a duty to notice, to investigate and to take appropriate action."
The ruling comes as a blow to LEAs which could be liable for hundreds of thousands of pounds in damages or, at best, steep legal fees. Peter Coles, the chief education officer for Hampshire, said: "We're fearful that the ruling could take educational funds away from youngsters with special educational needs." The allegation against Hampshire - that it negligently failed to deal with Mr Christmas's dyslexia - has yet to be proved and will be vigorously contested.
"The system is going to spend money on the legal processes rather than on providing for children's special educational needs," said Mr Coles. "We don't like throwing money at lawyers. We believe this is the most significant thing that's happened to education law since 1944."