Chandler Air Service in Arizona... BA fly direct from LHR most (if not all) days. They are SEVIS approved, frequently deal with foreigners etc and the scenery/weather beats Florida hands-down. They offer quality instruction in a variety of aircraft.
So go there = problem solved.
I can also recommend a FAA/EASA AME at Staverton airport who is very reasonably priced and will do both medicals in the same visit.
Should you want a Flight Review or IPC done here in the UK (in Northern England) by a FAA CFI/II in a C150/C172 at reasonable rates, PM me.
Regards,
Spr K. RE retd.