I'm pleased to tell you that's wrong. I can't post a URL but Google for "CAA Recognition of ICAO third country licences in UK airspace".
Thanks for that reference. Doesn't help me though as CAA requires a class 2 medical and, to fly the same aircraft in USA, I need only Class 3 or BasicMed.
The current rules are more stringent than when I went back to UK in 1982. At that time there was no limitation on how long I could fly on my FAA certificate and I was checked out to rent and to tow at my local gliding club.