Do not be intimidated by this school. They may seek to pursue a CCJ but to do that they have to raise court action for payment and you should defend such an action on the ground of breach of contract. It is implied in the contract you have with the school that they will not provide teachers that behave in this way. I think they have intimidated you. You should be saying to them, "go ahead, sue us, we will defend the action and the actions of your teacher and the school's attitude will end up in the public domain". That is the last thing they will want; for their incompetence to be made public. I think if you fight them you will win. I hope that helps. Please leave a positive rating so that I am credited for my time.
You need to see a solicitor immediately and if proceedings have already been raised by the school you do have to put in a defence.
If they have issued proceedings you need to get someone very quickly as writing a holding letter has no weight. We aren't allowed to recommend experts on this site but may I suggest you contact the Law Society for a recommendation of a civil court solicitor in your area.