Sam
you can do the whole thing if you want in the uk without going to USA. I now have my us piggyback credit card pilot certificate, covering my jaa sep and mep ratings, a current FAA class 2 medical and a current bfr. I have travelled no further than farnborough and it was most straightforward.
I very much want to go to USA and do some flying but this bit was done here.
Now have tsa clearance, done in Oxford, and just about to do written for FAA ir.
The FAA make it all very easy.
It can all be done in uk if time is important.