If you want a full FAA PPL the hours on your ICAO licence will count. You will need a class 3 FAA medical (can be done in the UK) and will need to sit the FAA flight test and written paper. You will also have to do night hours if you do not already have them as the FAA PPL alows night flying. You will also need TSA clearance for the test (even if done in the UK) and an M1 visa if you do it in the US.
Try Flight Saftey at Farnborough as I think they can do FAA writtens and will be able to guide you better.
You will then be able to fly any SEP land under 200 HP and not complex. High performance and complex are quite easy add ons after.
Your best bet is to call the FAA who will give you a definitave answer - they are really very helpful and a pleasure to deal with (in my own experience).
Hope this helps