Need some military input here....
Brize do seem to have some funny ideas about altimetry outside CAS. When we prenote inbounds, they normally allocate a height based on their QFE. Transits either get Brize QFE or the Cotswold, but they always ask for our QNH for inbounds. I'm guessing it's Unit specific procedures?
As far as I'm concerned you can use whatever setting you like in Class G, that is appropriate to your flight and I'm not entirely comfortable with the 'climb/descend and report level..xxx ft, on xxx mb' military phraseology under anything other than a RAS, but that's a whole other can of worms!!
In the situation you describe, I would have asked for the London QNH.
Notwithstanding the above, Brize do an excellent job with limited resources