So still around post war then. A lot of new clubs formed immediately after the war, when all the young fit folk came home and wanted an outlet for their energies. Not all clubs survived of course; if they failed then often some former members would move to other more mainstream clubs. Two possibilities there might be the Lancashire Caving & Climbing Club (which had a few members from that area on the list in the 1970s at least) or the Derbyshire Caving Club (which is, I think, essentially Stockport / Manchester based, so not far away).
If you really want to look into this seriously, archived newspapers from the early 1950s from that area might throw up something useful?
I'll keep pondering on it because I have a vague recollection of having read something about this group, a long time ago.