Mmmmmm. VERY interesting....
The 'FAA have shot down more aircraft than the RAF' line is frequently used - but of course, the point here is that the only air-air shooting war the UK has been in without the USAF was the Falklands. And the top-scoring pilot was the then Flt Lt David Morgan, RAF.
As for Korea, no RAF fighters were sent - but, off the top of my head, I think that several RAF chaps on exchange did get in amongst the MiGs with success. The RAF can hardly be blamed for lack of success when it was a political decision not to deploy fighter units.
I feel a letter coming on....