Much depends on whether you want to be an airline pilot, a business jet / corporate pilot, or a private pilot.
Simply, and in general terms, the country of your license issue has to match the country of aircraft registration, if you want normal UK+foreign flying privileges.
The UK operates an exception in that any ICAO license is good for a G-reg plane, flown worldwide. But nobody can say how long this will last.
If you are going to buy a plane and play this game long and seriously, getting an IR (without an instrument qualification, a basic PPL is close to useless for going from A to B) then an FAA PPL leads you to the FAA IR and if you buy an N-reg plane you are sorted. That privilege may also not last for ever (for European residents) but there are ways forward...
If you just want to rent, it will usually be G-reg planes and you are best off getting a JAA (UK) PPL. (Most flying schools will refuse to believe that you can fly their G-reg on any ICAO PPL). You can do this in the USA too but only in Florida, or one school in S. California.
There is indeed a process for converting an ICAO PPL into a UK/JAA PPL - it is somewhere in a publication called LASORS. It gets a lot simpler if you have something like 100 hours when you do it.
For foreign training I would recommend Arizona. Great weather, virtually no cancelled lessons. But no CAA/JAA approved schools so you would come out with a straight FAA PPL.
I've sent you a PM.