Timzsta - that sounds like self-employed to me too.
ewsd02 - I'd be a bit worried about that. Better if you can demonstrate that you have actually done some work for the 'other' school.
Of course there are probably plenty of instructors operating on a self-employed basis but only working for one school, and they will probably be ok unless HMRC decides to ask awkward questions. The problem is that HMRC are taking the view that if you only have one 'employer' you can't be genuinely self-employed. Personally I think that is a mis-understanding of self-employment - after all, we choose where to offer our services and how is that principle affected if we choose to offer those services to only one school? - but HMRC's view seems to be the way the law has developed, so it is as well to be aware of that I think.
BTW - No specific legal advice is to be inferred from this posting! (Sorry about that!)