You will need to do some digging to get your head around the rules on using your FAA licence in the UK and Europe - ie find the source documents and understand them rather than relying on what people tell you as most of them will get it wrong! The CAA website is a good place to start.
As a summary, you can fly privately in a G-reg EASA aircraft using your FAA certificate - this was going to come to en end in 2015 but has been extended for a couple of years. You can also fly a G-reg non-EASA (Annexe II) aircraft on your FAA ticket and will be able to continue to do so for the foreseeable future. You will have to check what privileges carry over from an FAA IR.
Don't forget that there are some Annexe II types (such as microlights) which the FAA recognise as "airplanes" for the purposes of hour building / experience but which EASA don't, so that can be a lower cost way to incrementing your hours.
My understanding on instruction is that for an FAA instructor to instruct on an N-reg aircraft in the UK you need permission from the DFT via the CAA. Don't know how it would work for an FAA instructor on a G-reg aircraft.
If you are thinking of hiring aircraft to hour-build then doing it in the UK would seem an odd thing to do given the difference in cost between UK and US.