Flying with FAA license in UK

[selfin]

Explanatory Note to Official Record Series 4, No. 1228. UK CAA.
Published on 27 June 2017. Superseded on 8 April 2019.

Although UK exemption E4433 enables FAA licence holders to fly using
FAA Class 2 medicals, it has since become clear that the Class 2 FAA
medical is more akin to an EASA Class 1 and that the FAA Class 3
medical is the closer equivalent to an ICAO Class 2, which is the
minimum medical expected for the purposes of recognizing Third Country
Licences in Annex III (4) (d) of Part-FCL. It is also clear that the
general exemption made available by EASA, with the European
Commission’s agreement, permits FAA licence holders intending to fly
non-commercially, using private FAA licence privileges, to continue to
do so using Class 3 FAA medical certificates. UK medical opinion
indicates that such Class 3 FAA medicals are broadly equivalent to
ICAO Class 2 medicals.

Further, the United States AIP GEN 1.7 (Differences from ICAO Standards, etc) states for annex 1 chapter 2 reference 2.3.1.4:

U.S. private pilots required to hold an FAA Third-Class medical
certificate must meet the requirements of an FAA Third-Class medical
certificate which are equivalent to ICAO Class 2 with exceptions
specified in Chapter 6.

The same is true for the Canadian Category 3 medical which is equivalent to an ICAO Class 2 Medical Assessment.