Depends ...
If you mean by an RAF pilot in an RAF-owned plane then you can either choose the Confrontation with Indonesia (Jackonicko has alluded before now to some evidence to suggest that an Indonesian aircraft was shot down by, I think, a Javelin). Failing that, WW2.
If you mean by an RAF pilot, then I think the Falklands, when RAF bods on loan to the SHAR force did rather well. Also a number of victories gained by RAF pilots in Korea on exchange with F-86 outfits and, I believe, with 77 Squadron RAAF.
And stand by for the umpteenth airing of comments about the accidental shoot-down of the Jag by the Phantom...
Edit - oops. Forgot about the little fracas with the Israelis and the Egyptians in 1948. Couple of losses and a couple of victories there. Also, a Canberra was shot down during the Suez crisis, and a Valiant detected the emissions of something - probably an EAF Meteor NF - stuggling to try and reach it (it didn't).