As a self-employed freelance instructor who is vat registered I can correct a few misunderstandings...
You do not have to register a limited company to be vat registered. I operate my business as a "sole trader". The words "sole trader" have a particular meaning for inland revenue purposes. For example, your business can have employees whos wages you pay, but still be a "sole trader" for taxation.
Because I am vat registered, I can claim back the vat on business expenses, but I have to charge vat at 17.5% on all my invoices. This is no problem when I do work for any flying school, because they can in turn claim the vat back, so I am no less competitive than any other freelance instructor.
However, when I charge students directly for instruction, for example when an owner is converting to a new type, I absorb the vat and quote a vat-inclusive rate to the student. In fact I don't even mention vat to the student, but I have to hand nearly £15 in every £100 over to Customs and Excise.
Overall, I choose to remain vat registered because it suits the way I work and it suits the companies which provide the bulk of my income.
With any vat queory, the best plan is to telephone the vat helplines. Contrary to popular belief, I have always found them very helpful and straightforward to deal with. However, I always write notes of the conversation at the time, and always get the full name of who I speak to.
Finally, if you are just starting as an instructor, I wouldn't think it worth the extra paperwork to become vat registered, and it will not be relevent to you if you get employment (c.f. freelance work) with a flying school.