I hope somebody clued-up posts a detailed answer, but basically the process would be this:
There used to be a CAA-FAA treaty for mutual certification, so most STCd parts could be fitted to a G. You had to get an AAN from the CAA though.
The CAA AAN database on online at the CAA website, and those items should be fittable straight away.
That's a start.
If there is no AAN, the next thing is to try to trace somebody else elsewhere in Europe who has got a local CAA approval. I am not aware of other online databases but if you ask the manufacturer of the part for details of other customers in Europe, that should start you on a trail.
If there is no traceable previous approval anywhere at all, you have to do it from scratch and that I know nothing about (being on N-reg now). I believe there are companies approved for the certification; effectively this will get you an "EASA STC" but certainly under CAA they used to charge a lot, four figures just to look at anything.
Under EASA, it cannot possibly be any worse that ithas been in the past
But they are slow getting going.
Most things are easier under FAA, largely because of the much wider range of approved parts on the market. Major mods are still expensive but not as silly as under CAA. A further advantage of FAA is that there is more discretion as to the classification as to what is a major or minor mod, etc. I was once quoted £2000 for installing an ELT on a G, about half that on N on a 337+DER signoff (identical product and circumstances) and later I found an even easier route on N. On the other hand, if you operate an N in the UK they see you coming, assume you are loaded, and jack the price up... so having good contacts is key.