There are many FAA CFI instructors over here in the UK and Europe.
Any of them can do a BFR.
For an IPC you need a CFII but nearly all CFIs are actually CFIIs.
The issue with paying the instructor is a separate one. In UK airspace, if he is paid for the flight, he should have a UK/JAA CPL.
In practice this is not an issue since many pilots (myself included) have friends who are FAA instructors and who do it genuinely for free. I know a whole bunch of A&P/IAs, ATPs, CFIIs, you name it - all working in aviation somewhere. All of them can do anything on a purely freelance basis. It's a great system.
There are some dual (FAA & JAA) rated instructors but not many. In the past, I found them unavailable when I needed them as they were very busy.