I must confess there is no simple clear statement that a UK licence issued in accordance with Part FCL is now a UK Part FCL licence.
Whilst searching, I found the following statement on the CAA website:
From 1 January 2023, the UK can no longer recognise EASA-issued licences.
Gaining a UK licence from 01 January 2023
Pilots are required to hold a UK licence to fly G-Reg aircraft in the UK.
Then if we look at Article 150, it contradicts that statement:
Art 150.— Deeming a non-United Kingdom flight crew licence and any Part-FCL licence valid for [ non-Part-21 ] aircraft registered in the United Kingdom and deeming a non-United Kingdom radiotelephony licence valid for any aircraft
No wonder people are confused