Annie Woodland was a pupil at Whitmore Junior School in Basildon, Essex, when she had to be pulled from the water and resuscitated at Gloucester Park pool in 2000.
Miss Woodland, now 22, now has severe learning difficulties and her father, Ian, has launched a claim for compensation on her behalf against the local education authority, Essex County Council.
Proceedings have also been brought against the Swimming Teachers' Association, Beryl Stotford - who traded as Direct Swimming Services - lifeguard Deborah Maxwell and Basildon District Council, which ran the pool.
At a preliminary hearing, lawyers argued that Essex had a non-delegable duty of care "in the capacity loco parentis".
They asserted that the authority was vicariously liable for the alleged negligence of both Ms Stotford and Ms Maxwell, and directly liable for failure itself to take reasonable care to ensure that Ms Stotford was an appropriate and competent independent contractor to whom to delegate responsibility for the provision of swimming lessons and life-guarding services.
Essex denied that it was vicariously liable for any want of care on the part of the lifeguard or that the duty was non-delegable as alleged.
In October last year, High Court judge Mr Justice Langstaff, sitting in London, threw out Miss Woodland's claim against Essex on the basis that it was bound to fail, and today that view was backed by a majority of judges in the Court of Appeal.
Lord Justice Tomlinson and Lord Justice Kitchin said that in all the circumstances, it would not be fair, just or reasonable to impose the non-delegable duty upon the authority.
And, said Lord Justice Tomlinson, the imposition of such liability would be likely to have a chilling effect on the willingness of education authorities to provide valuable educational experiences for their pupils.
It would have significant implications not just for all education authorities but also for all those who operated schools and hospitals and, he suspected, all those who operated institutions which provided what might loosely be described as education or healthcare.