The FAA accepts non-US training from anywhere in the world, so all of your old JAA training counts.
You will probably need to do some specific night flights, because the FAA PPL has night privileges as standard. Check the FAR/AIM.
Then
- FAA medical (can be easily done in the UK)
- FAA PPL written exam (Flight Safety at Farnborough)
- 3 hours min with an FAA CFI instructor within the last 60 days of the checkride
- the checkride itself
The last bit is a little tricky in Europe, and most people go to the USA for the last two items, having done the other stuff in the UK. Unfortunately, you do need TSA+Visa for the PPL, ME or IR.