You can fly G reg aircraft in England with an FAA PPL. It gets complicated if you want to fly one out of UK airspace though. You can fly N reg aircraft on an FAA PPL just about anywhere within normal flight rules and airspace usage rules. In other words, don't cross borders without proper authorization, stay out of restricted airspace, etc.
As with anything aviation related, make sure you know the rules inside out and don't just take someone's word from PPRuNe. I assume you are in the early stages of research, so please learn the rules cold before you actually do whatever it is that drives your question. I doubt anyone will rent an aircraft to you without thorough briefing, but in the end, you get the violation if you bust the rules, not them.