VFE, Its really very simple. I am a VAT registered instructor. At the end of each month I give each flying school, (I work for several) a vat invoice, which is just an invoice for a certain number of instructing hours at the rate the school pays all its self-employed instructors, and the total then has 17.5% vat added.
Yes the school has to charge vat on lessons, and it doesn't matter if the particular instructor is vat registered or not, the customer still has to be charged vat at 17.5%.
The only downside to being vat registered (apart from the small extra paperwork) is that when I work directly for a customer, e.g. type conversions in customer's own aircraft, I still have to charge vat. In practice, the customer doesn't know this, or care, because I charge a vat-inclusive price. It does, however, mean I get 15 % less in my pocket on these occasions. However, I balance this by getting the vat back on extra training and renewals.
Whether it is worthwhile or not depends on your individual circumstances.