OK. You go to the Flight Standards District Office of the FAA and present your licence and logbook/medical etc. You will be given an FAA certificate which is based on your Caa/Jar one and with which you can then fly, subject to an insurance/rental check out by your rental club/school. The latter is not an FAA requirement nor is a Bfr seeing as the Faa just gave you the licence.
BUT!! In 2 years time if you want to continue to use your FAA licence, then you must have an FAA Bfr AND your Caa/Jar licence must also be current, in order to be legal.
This also applies outside the USA if flying using your FAA licence(N reg aircraft in Europe for example)
Why not go straight to a decent flight school, sign up for an accelerated Commercial single engine course and get yourself an original issuance FAA certificate not based on any other licence?
You can then add an instrument rating to it and do training for this in the UK and even sit the check ride over here if you want.
Just a thought. Should take a week to 10 days and its good fun.