I have no idea why the Hovercraft museum ended up at Lee on Solent, (except, maybe, because it had the space and was within 20 miles of where the modern hovercraft was developed).
The modern hovercraft was developed on the Isle of Wight by Saunders Rowe from the designs of Sir Christopher Cockerel, so Wikipedia tells me, (and from what I remember).
Sorry to put a serious note in here, but you did ask.

Sorry. But it looked similar to the Hovershow.
Any ideas why the ended up at Lee-on-Solent?
regards, Dave