The Footlights Dramatic Club

Founded 1883.

The obligatory famous members list
Jack Hulbert, Richard Murdoch, Jimmy Edwards, Cecil Beaton, Frederic Raphael, David Frost, Jonathan Miller, Leslie Bricusse, Peter Cook, Clive Anderson, David Hare, Richard Eyre, Eleanor Bron, John Bird, John Fortune (John Wood), Germaine Greer, Miriam Margolyes, Clive James, Tim Brooke-Taylor, John Cleese, Eric Idle, Graham Chapman, Bill Oddie, Graham Garden, Douglas Adams, Julie Covington, Shephen Fry, Hugh Laurie, Griff Rhys-Jones, Rory McGrath, Jimmy Mulville, Jan Ravens, Sandi Toksvig, Neil Mullarkey, Chris England, Andy Parsons, Henry Naylor, Nick Hancock, Emma Thompson, Hugh (Peter) Dennis, Steve Punt, Tony Slattery, David Baddiel, Morwenna Banks, Richard Vranch, Sue Perkins, Mel Giedroyc, Alexander Armstrong, Ben Miller.

The non-members list (many were at the Other Place) - people one might think were members but weren't
Dudley Moore, Terry Jones, Michael Palin

The Club room (1960-1972):
Don't Panic (Neil Gaiman's book about the story behind The Hitchhiker's Guide To The Galaxy) mentions it a couple of times: (p16) "redeveloped into a shopping centre", (p19) "knocked down to build a car park".
It was in Falcon Yard, was one of the many low-rent University clubrooms in the old streets and yards behind Petty Cury until 1972.
Clive James' May Week Was In June describes his time in Cambridge, much of which was taken up with Footlights. He explains the Club Room was above Macfisheries - with the consequent pong.
The premises were provided by the Arts Theatre Trust, who used the space for rehearsals and as a supplementary bar.
From 1978 Footlights has used the cellars of the Union Society.