three routes are possible
1. If you have any ICAO compliant licence that is valid ( ie in date, even if you don't meet currency rules) you can get a 61.75 FAA private certificate. You will have to go through the verification process - I'd suggest using your UK licence, (converting it to easa while you are at it which can be done on the uk caa website) because the UK caa are moderately efficient at replying to foreign requests (eg FAA) . You will need to appear in person to a DPE ( eg the guy mentioned above in UK), or take a trip to a US FSDO. You will need a valid medical - you have the option of verifying and using your medical that matches the licence you are verifying or getting a new FAA 3rd class medical. ( and FAA 3rd class is probably less arduous and more generous with issues than most) You will need a flight review (BFR) before being able to excercise the priviledges of your certificate.
2. You can get a FAA PPL by following the same route as any student. Written, checkride, etc. You will meet the hours requirements. You will not need an endorsement for the check ride, and thus theoretically don't need TSA. Lots of people will tell you otherwise, but that is the case. This is more work but you get a stand alone licence. I have done this.
3. Fly day vfr in an N reg using a licence applicable to the country you are in if that country allows it ( eg the UK)
Pace - that might work for you. At least until april 2016.