I suppose it would be foolish not to mention the great piece Tony Paley did on London Film Nights, while certainly by no means comprehensive, solid and covering a good range of evenings.
From our friends at Filmbar70 and their classy approach to cult films to The Duke Mitchell Film Club and their treasure troves of trailers and the down right bizarre cult films to the Exploding Head Film Club and Tom's love of American Cinema, not to mention ourselves. I think Tony did a great job.
London has a near endless supply of film nights, some pop up for a few weeks and others stick around for years, but if you want to, you can catch a film and a pint almost every night of the week.
Anyway - have a read, come down to each of the nights mentioned, wander through the comments where even more are mentioned.
Film Clubs: Fancy a Cheap Night out at the Picture and a Pint?