CAA website it fine. You just need to know where to look!
You need an FAA ticket to fly in the US; if you don't have any licence that will need to be a Medical/Student Licence; they can be for FAA Class 1/2/3.
If you then go on to get your FAA license with that you can fly with that FAA license and medical either in the US or in the UK.
The FAA medical/student licence does not validate your UK PPL; for that you need a UK Medical.