'Mosquito' is a term used for aircraft flown by the USAF 6147th Tactical Air Control Group (T-6s mainly I recall), operating as forward air controllers. The first MiG-15 sighting in Korea was by one of these 'Mosquito' T-6s, and at least one documentary erroneously portrayed that incident with footage of a DH Mosquito.
I think that documentary (and the use of 'Mosquitos' in Korea) is where this confusion began.
By the way there was a lot of direct RAF involvement in Korea - aircrew saw first-line service in F-84s and F-86s for example.