Presumably sometime prior to the 1960s, when "Base Hangar" was built.
I should imagine it goes hand in hand with where fleets are "based".
Has the term "stationed" ever been applied to aircraft fleets? I wouldn't think so, only to personnel, and possibly units. "The Canberra was stationed at many RAF stations" sounds wrong.
Perhaps a "base" suggests more of a "Main Operating Base" than a backwater. Thus closing Brize Norton (as a MOB) would be much more far reaching than closing the RAF station near Formby, RAF Woodvale. It's a bit (lot!) of a stretch to call it a "base". Or to put it another way, Coltishall was a base closure, Sealand a station closure, even though Coltishall was indeed a Station.
Does it really matter? If this is right, there will be three less of them. That's what matters.