I did this with my JAR PPL(A) a few months ago. General procedure was...
- Download FAA form, send to FAA applying and stating which FSDO you want to get your licence from.
- Download CAA form, send to CAA with £15 asking them to release your details to FAA.
- Wait about 3 weeks for letter from FAA saying "yes, we'll give you a licence"
- Phone appropriate FSDO, book appointment (they only need a couple of hours notice, it's a security thing I think).
- Turn up with JAR licence, CAA form, letter from FAA.
- Get issued on the spot (took about half an hour) with a 120 day temporary licence. Nice man at the FSDO told me all about the local spots to fly as well.
- About 110 days later, shiny new FAA licence (with a picture of the Wright brothers on the back) arrives in post validating your JAR license in the US.
Presumably it's much the same for a PPL(H). Slow, but (apart from having to visit the FSDO in person) basically painless.
G
N.B. Unless it's changed recently, I believe that UK CAA will allow any ICAO PPL holder to fly a UK registered aircraft for which they are rated, in UK airspace, but day-VMC only.