The UK CAA will allow you to fly either a N-reg or a G-reg within the UK on your FAA license. However, if you plan on flying abroad you can not legally fly a G-reg with a FAA license outside the country, only the N-reg (there are a good amount of those there).
Couple of points:
Flying in the UK is great, but just remember that airports are not subsidised like in the US, so you will have a landing fee. It varies from £10 up to £highwayrobbery depending on size of field. The smaller the field, the cheaper, usually. Many fields are grass, so get up to speed on your soft field takeoffs. Many smaller fields are PPR, so you need to call them and tell them you're coming.
Joining procedures are different than in the US and you will get screamed at if you do the 45-degree join. Read up on overhead joins, it's what they use unless otherwise specified. Also, a pattern is called a circuit. "Cleared for the option" means nothing to them, so don't ask for it.
You'll also encounter A/G airfields, where A/G stands for Air-to-Ground. It's basically an advisory radio service - they will recommend you the best rwy and give you directions, but they can't give you a clearance. Think of it as an uncontrolled field where a controller gives you good advice.
Pilot controlled lighting doesn't exist, so flying into smaller airfields is a daytime operation only and most airfields have operating hours. You can not legally land after they're closed unless you have a special indemnity approval. The bigger ones will be available at night, but the landing fees will be costlier.
All night flying is IFR compliant (although you do not need to be IFR rated), so you need to fly at the right altitudes and file a flight plan. IFR flight is legal in class G airspace there - and class G goes much higher than in the US. So watch out, you might not be the only one in that cloud not talking to anyone. There is virtually no class E airspace and no B. Transition Level varies and is not 18000ft like in the US, so check the local TL before you go flying IFR. It's normally around FL050 or thereabouts. Class A airspace can go to the ground around big airports (like Heathrow), so don't go bumbling into it or you're in trouble.
VFR squawk in Europe is 7000, not 1200.
I would suggest buying SkyDemon app which is like the Foreflight of Europe. If you prefer printed stuff, get Pooley's Airfield Guide.
