You may apply for a foreign-based US private.
First, the UK licence and medical need verifying. Complete instructions are here,
https://www.faa.gov/licenses_certifi...e_verification
Once the verification has been done, you may apply for the US pilot certificate with a DPE (fees vary) or at a FSDO (free).
Before exercising PIC privileges you’ll need to do a flight review with a US instructor. You may this in the UK before the above steps if you wish.