I think that you may be getting over-cautious replies here. The particular issue is with STC's and Major Modifications (form 337) fitted to the aircraft.
Firstly, if there are no mods, or very few mods, fitted to your chosen aircraft then it's probably not really an issue at all.
If there are some major modifications (like a different engine, a retrofit glass panel, whatever) then the question is whether the same mod has ever been approved in Europe. In the olden days (pre EASA) then any mod had to comply with the airworthiness criteria of the country you wanted to register it in. So, to register in the UK, you either need to reapply for that modification, or if you are lucky, find someone else in the UK who already has that modification approved. But now we are in the EASA world, and the new rules have grandfathered anything that was already approved in ANY of the EASA countries. So you don't need to find evidence that the same modification has previously been approved in the UK any more - instead you just need to find evidence that the same mod has been fitted to ANY aircraft ANYWHERE in EASA land. And, since many smaller countries routinely rubber-stamped FAA STC's, the reality is that most of the popular STC's, including ones that the UK CAA had previously rejected as being completely unacceptable, are now perfectly legal EASA STC's.