Not sure what the UK regs require on the use of N-registered A/C. But when you are flying an N-reg A/C, you are doing so under the authority of your FAA CPL, not your UK PPL. In fact, you CANNOT operate an N-reg aircraft legally under part 91 with a UK PPL. It must be converted or co-validated with a US certificate.
But BFR/IPC by an FAA CFII in an N-reg, for compensation, no matter where it's conducted, is legal under US regs.
Also, BFR and IPC are NOT 'training.' They are proficiency checks that can be endorsed by an appropriately rated instructor.