I guess Google is still my friend.
Came across this regarding fast-tracking:
https://www.caa.co.uk/General-aviati...unter-service/
Does not state anything related to transfering OUT of the UK - and I know that the process technically starts from the receiving country initiating the process.
I presume I may not be able to expedite anything - at least not until the other country starts the process.
Transfering from the UK (at the bottom of the page):
https://www.caa.co.uk/Commercial-ind...licence-issue/