I rent G-reg aircraft in the UK on an FAA ticket. In my experience of 3 flight schools, they are a little reluctant and likely to insist on "UK differences training" (unnecessary IMO) but will rent you the aeroplane. They are more reluctant to let you take it outside of the UK, which you are perfectly entitled to do VFR, but again after explaining the letter of the law it was okay.
To be strictly legal you need to get a radiotelephony operator's licence (think that's what it's called) from the FCC, which takes a few minutes online and $20. This is the R part in ARROW which you need if you want to use your FAA ticket outside of US airspace.