Reading the question, if what you are after is a standalone FAA ticket, the answer is slightly different to Genghis' who describes very well what to do if you want the restricted one (except the CAA Fee has just gone up to £16)
To get your own FAA PPL you need to:
1) Obtain an FAA Class 3 medical
2) Sit the FAA PPL Knowledge test
3) Brush up on your general flying and in particular, your ground reference maneuvers[sic] (not part of the JAA PPL), ideally with an FAA instructor. You will need an FAA instructor's sign-off that you are ready for the Oral and Flight test. Such a sign-off can only be given to a student the instructor has actually taught.
4) Take the FAA Oral Exam and Flight test
1 and 2 can easily be achieved in the UK. So can 3. In principle, 4 can too although opinions vary about how often visiting FAA examiners come to the UK and how easily slots can be booked.
Personally, I would probably get a cheap flight out to the US and do 3 and 4 there. The only downside to that, is the need to obtain an M-1 visa, which is not nearly as painful as some suggest. I now know several people who found it far more painful (and costly) keeping topped up with training whilst the FAA examiners were due to turn up in the UK "next month".
PM me if you want more specific advice.
2D