Here's a link to the UK's ship registry
UK Ship Register
In an nutshell, there are two sorts of registry for yachts. Part I and Part III.
Part I is the main one as used by ships etc. It also shows if a mortgage has been raised against the vessel. Who owns it and in what proportion. To get on this registry you have to show an unbroken series of owners from the original builder to the present day. The usual method of proving this is by the "Bill of Sale". Also, the boat has to be measured by an approved surveyor for tonnage measurement.
As you can imagine it can be quite expensive. My moat came Part I registered and I've kept it up.
Part III is a completely different animal. It really doesn't mean very much apart from giving you a bit of paper to wave at foreign officials. You can do the forms on-line.
Sorry I don't know about the VAT implications for a non EU residents. You could try searching on this forum for suggestions.
Yachting and Boating World forums: Viewing forum: Yachting Monthly's Scuttlebutt
I warn you the search facility is pants so don't be afraid to start a new thread.