Given the size of the fee, it's probably a special independent school as opposed to an ordinary school.
You may also find, given the circumstances, the child has a Statement of Special Educational Needs & other mainstream schools have simply refused point blank to take her on, or the Authority's own special schools couldn't accommodate her.
Blaming the parents isn't the answer neither is dumping so called disruptive children in special schools & isolating them. There are plenty of mainstream schools out there who fail children by refusing to acknowledge their problems and acquire the necessary help at an early enough stage. In my experience, there are also plenty of schools who simply don't want to deal with disruptive children, label them & then do their damndest to shunt them out of the school & make them someone elses problem.