I'll have a look into it, but I'm an audit accountant, not a tax accountant.
I was however under the impression that flying was VATable, since the Chancellor deemed that all flying training was the pursuit of the rich and wealthy as leisure, despite of course CPL and ATPL being professional.
Obviously there is something wrong with that reasoning, as Johe02 has a different account, however being VAT registered as a person and not an entity does, I believe, entail some problems if things are not done by the book.
If you are the direct employee, you are definitively not able to claim VAT, since by rights, you are not an outside consultant, and the majority of the working year will be spent working as an instructor. If however it was freelance work, going from school to school, some surely could be claimed back in respect of training, and additionally VAT charged.
Basically if HMC&E say there is a hard ruling, or indeed do the Inland Revenue, double check, since they do not have the best reputation for wholly honest and impartial advice. Indeed check your tax return, as they are invariably wrong!