You've highlighted something that I'd not noticed before. I have a UK PPL and a (was) EASA PPL, both with FI and CRI on them. The bit I've not noticed is that the UK PPL does not include FCL.945 but the EASA one does. They've both been re-issued a couple of time since CAA started printing 'FCL.945' on them, so I reckon Whopity is correct, in that CAA policy has probably been to not include it on UK (non-EASA) licences.
As an adjunct I have an 'R Examiner' approval via the LAA Coaching scheme which, as far as I can tell, is the CAA equivalent of the FCL.945 authorisation. I wonder if CAA would simply issue instructors with 'R Examiner' authorisations outside of the LAA Coaching scheme? That would seem to be a workable answer.