London Belongs to Me (aka Dulcimer Street, 1948).

Sketch by H. R. [Roy] Oxley for London Belongs to Me

Encountering gamblers and murder in London Belongs to Me are eccentric boarding house residents (such as car thief Richard Attenborough and dubious clairvoyant Alistair Sim). The film was adapted from the novel by Norman Collins (Dick Barton: Special Agent) and directed by Sidney Gilliat (well known for his screenplays for The Lady Vanishes and Green for Danger).