Put simply, it is dodgy (under what appears current aggressive HMRC practices) to put an aircraft into a limited company, because of the Benefit in Kind rules.
Unless the company is set up as a proper full rental business, starting with a documented business plan (yes I know BPs aren't worth the paper they are written on but that's besides the point), a booking site ensuring equal access to all, etc. Miss out on any of these features and the employees/Directors better not go anywhere near any of the planes (better not even have a PPL, actually, because BIK is charges on access even if no private use actually took place) otherwise they are likely to get hit for Benefit in Kind.
There is little point in VAT registering unless you expect the rental revenue to exceed the mandatory reg limit (£55k?). Otherwise, you have to invoice VAT and that makes the flying 17.5% more expensive. Find a hangar owner, maintenance outfit, etc, that doesn't charge VAT and there is no need to reclaim it. Regards any VAT on the initial aircraft purchase, it's best to do it via Denmark.
The case I wrote about a while ago is probably going to the commissioners, but it's taken 18 months already.