You can fly with an FAA certificate. My personal experience was that this is not well understood by most UK flying schools. You will be put under pressure to convert to a JAA licence, and if you stand your ground, many places will turn your business away.
There are schools that will rent to you, just phone around. Procedures are different and you should take time to familiarise yourself with them and have a sensible number of hours instruction. Then go have fun flying not above 2000ft
