This film (also being shown on August 14th) is part of an Ingrid Bergman on screen season at BFI Southbank. Full details here.
Chicago Reader review:
Part of what makes this wartime Hollywood drama (1942) about love and political commitment so fondly remembered is its evocation of a time when the sentiment of this country about certain things appeared to be unified. (It's been suggested that communism is the political involvement that Bogart's grizzled casino owner Rick may be in retreat from at the beginning.) This hastily patched together picture, which started out as a B film, wound up getting an Oscar, and displays a cozy, studio-bound claustrophobia that Howard Hawks improved upon in his superior spin-off To Have and Have Not. Then again, we get Humphrey Bogart, Ingrid Bergman, Claude Rains, Paul Henreid, Conrad Veidt, Sydney Greenstreet, Peter Lorre, Marcel Dalio, and S.Z. Sakall, and Dooley Wilson performing "As Time Goes By."
Here (and above) is the trailer.