CZBB,
I'm not too sure how easy it is to rent G reg aircraft in the UK with an FAA Private. I can't see why it would be a problem as long as you stay within UK airspace, and you have a good checkout. N reg is not a problem, although there are obviously not so many of these around. Popham hire to FAA , but am not sure whether they are G or N reg. I'd be interested to hear if anybody knows for certain the logistics involved in hiring G reg with FAA Private.