From memory when operating my old flying club's A/G radio, I only ever used "Red Arrows" to/from them (sadly only while they were in transit, courtesy call to let us know they were there really). BBMF a/c usually called initially as BBMF-type following which we would shorten it to type only (eg initial call BBMF Spitfire, reduced to Spitfire). I seem to recall the Vulcan only ever called us as Vulcan too. Used to get a privately owned Mustang that called up as Mustang-full reg which we then shortened to Mustang after the initial call.
All from memory, don''t do the A/G stuff anymore.