I don't believe that Fighter Command recognized an aircraft mission outside "interceptor" for fighters.
The big problem being an organizational one in the RAF. RAFG and the other commands (MEAF, FEAF, and I am missing one) that needed capable ground attackers etc didn't have a voice with the same authority as Fighter Command or Bomber Command. Fighter Command being the RAF equivalent of USAF Air Defense Command, Bomber Command being our nuclear friends.
The USAF had SAC, TAC, ADC, and MAC, each as a separate organization of roughly equal power. Bombers and ICBMs, fighters and ground attackers, interceptors and missiles, transports and tankers. Each one had its own Star-in-charge to argue for it.
But the RAF didn't have an equivalent to Tactical Air Command, even though everyone who heard the name "Fighter Command" thought that it was that equivalent.