The Governing Body is the appropriate forum for complaints. Unfortunately they very seldom do anything, as they feel duty bound to support the Principal. Moreover, the Principal attends meetings as an ex officio member. Ultimately, there is nothing you can do in relation to a private school apart from withdraw your son and find some alternative establishment where he will be happier.
One of my sons was excluded for health reasons in the middle of his GCSE course and I explored every avenue before realising that there was, in fact, nothing to be done apart from damage limitation in the form of finding another school. In fact, he did well in his exams and helped push his new (much kinder) school up the league table.
Edit: I realise that this is the new type of institution which is state funded. I can only suggest that you get in touch with these people as being in overall charge (as far as that goes) and ask for advice as to what to do next. http://www.standards.dfes.gov.uk/academies/mailbox/?version=1