Guys you should really speak to an accountant who would be able to advise you properly. Starting your own 'business' just to invoice the flying school you effectively are employed by can get quite complicated, search the HMRC website for IR35 and see what pops up.
Again remember the difference between VAT and the income tax that you have paid on the money that you are paying out for your training. It is not really the taxpayer funding your training in any sense of the word it is just deducting your training expenses from your income.
Speak to someone in the know who will be able to advise you properly!