British Airways previously had a club based at Booker and Britannia Airways (later TUI) had a club operating from Luton before moving to Cranfield. I do not believe either are still linked to their airlines although the aircraft were still carrying the airline colours, at least until recently.
There is also a very smart PA28, G-RECW, which has recently been repainted in British Caledonian colours. This seems to be based at Blackbushe.