If you are resident in the UK, you are required to have a UK CAA licence for flying in an N-reg aeroplane in UK airspace. Once you cross the channel to EASAland, you're of-course fine as you're a non-EUian, flying an American Aeroplane on an American Licence.
EASA brought in a similar regulation so a European Citizen with an N-reg aircraft has to have an EASA licence for the flying they do in EASAland airspace, but then can fly it on their FAA certificate in UK airspace.
This has been the case since June 2022 in EASAland and December 2021 in the UK.
So, a British resident holding only FAA certificates, has not legally been able to command N-reg aeroplanes in UK airspace for the last 22 months or so.
G