Some staff and governors have left because they cannot take any more. We have made all possible allowances and not indicated our concern in any way up to now, but I am getting the clear message from my colleagues that they want her to go. What do I do next?
You cannot safely embark on the dismissal of a headteacher out of what is, to all intents and purposes, a cloudless sky. The fact that the problem is of long standing is irrelevant if the aspects of her behaviour which are unacceptable have never been discussed with her until now, even though dismissal in a GM school is possible after due processes for misconduct, incompetence or any other serious cause.
Grant-maintained schools are required to have a staffing committee; it is this committee which should carry out any investigation. Other governors should not be involved: this is essential in case an appeal has to be heard. The governors who took the action cannot also determine an appeal.
In a case like this, you cannot do anything unless the matters at issue have been logged over a period. I assume that you have some disciplinary procedures in place and I am sure they will have the elements mostly found in such procedures, namely provision for informal warnings, formal warning, formal written warning and, at every stage, targets for improvement and the possibility of clearing the record and a fresh start.
At all times the staff member must be clearly told what the problems are and given a chance to attend meetings (with a friend if desired) and to reply to complaints. These processes are common to most disciplinary procedures because they are the kind of things which an industrial tribunal would look for if asked to consider a wrongful dismissal. It is possible for a tribunal to rule a dismissal wrongful on procedural grounds - even if the merits are not in dispute, which could be expensive for the employer. The principles mostly derive from a code of practice drawn up by the Arbitration and Conciliation Service (ACAS) under employment law.
I cannot help feeling that it is a pity everybody has been too nice to challenge your head's behaviour sooner. It would be kinder in the long run to indicate that it is not acceptable. Is it too late for you to approach her informally? The road you are setting out on is full of pitfalls, and you should really only take it if you are sure you can't solve the problem by other means.