VAT yes we all hate paying it. You will have to pay VAT not only on the plane (based on cost price if new) but also the shippping costs.
I assume you we be putting it on the G reg, if not forget it you can't claim the VAT as input (cos you don't own the plane legally, the trust or US bod does).
As for claiming any VAT back on imports (something I do all the time) . Be it a plane, car, boat or blow up doll. It must be used for some business use afterwards. Otherwise whats left of the Customs and Excise force will look into you and everything you've done since you started shaving. (know someone who's been to the high court with them and is now trying to raise 160 K to keep his liberty).
So its best done with an existing business. Otherwise you are going to have to rent the plane out and charge VAt on such, to every pilot, even yourself. Yes you claim it back on Fuel, maintainance and other rated costs. But would it work out cheaper in the long run.
The short answer would be to operate it as a business for a period, say 3 years. Advertise it for hire (but you could make the conditions or costs prohibative for others). Charge the company lots of interest for the loan to buy the plane, plus management fees etc. Then when the company hasn't made a bean in that time, declare it insolvent and sell the plane back to yourselves for it book value (you can depreciate it at 25 % per year).
All in all a lot of hasle to save what £ 20k tops. Besides with the wierd VAt issues on selling used planes, you could pass that on to the next owner. ??