Bere
As I understand it, ALL the requirements for licence issue need to be undertaken under the guidance of any one "JAA member state".
So, the all minimum flight training (25 hrs dual, 10 hrs solo), all the written examinations (6 of them, I think), the final "skill test", the medical and the licence application must be done through one "country".
If you choose to do the course in the USA then this must all be done through the UK CAA - for the reasons you state.
This means that you require a UK medical (class two will suffice for PPL). You can get this class 2 medical by one of four methods - a CAA approved medical examiner in the UK (known as an 'AME'), a CAA AME in the USA (there are two - one in Florida, one in Michigan), a CAA approved AME in any country (don't know any - look at the web site)...or, go to a JAA AME anywhere in the World, get a copy of the medical reports taken by that AME and send them to UK CAA in Gatwick. They will then issue you a UK JAA medical.
If you want a class one medical - your only choice is to go to Gatwick and do it with the CAA themselves.
If you do decide to go the UK CAA way in the USA you may be required to take a seventh written examination (Radio theory) and a Radio Practical Test - for which you will need a good command of the English language.
If you do the medical, exams and flying in the USA then your application for licence can be done by mail and you need never go to the U.K.