I am not 100% sure, but as your UK (CAA) PPL is (or should be) perpetual, you can use it to gain a stand alone licence. I can't recall the exact training requirements, but it is somethingline you must to a min of 3 hours dual to prepare for the flight test, have flown at least 5 hours under instruments (can be dual) and of course, get your US medical. I don't think there is a theory requirement or whether you need a current medical from the country of licence.