I learnt to fly there back in 1987 doing all my PPL ratings including a twin rating. My membership lapsed back in 1994 after disappearing off to fly the big stuff. It was originally started up by a number of Armstrong Whitworth employees from the factory at Coventry, who wanted to learn to fly. They started with a single Tiger Moth I believe. The original clubhouse used to be adjacent to the car park along side The Oak pub in Baginton, but has since been moved with the regeneration work carried out at the airport.
All members are shareholders in the group and it used to have the cheapest rates for flying instruction certainly in the Midlands, if not the UK, when I was a member. The instructors were not renumerated for their instruction, it was all done for the love of flying and the social atmosphere that had been generated at the group. When I commenced my flying training there they had two C152's, G-BFOE and G-BNXC, but borrowed a few others when these two were off on maintenance, G-BNOZ is one that springs to mind.
Most of the flying is done at weekends or bank holidays, so for more information, I suggest a visit to Baginton, you are sure to be warmly welcomed with a cuppa. The CFI I believe is still John Stockley a patient and helpful instructor.
Hope this gives you some gounding on where to find the information you need.