“Boy who cried wolf” film about a man who confesses to every murder then commits one himself

Black and white British (I think) film- man confesses to every murder for weeks until he gets the local police to tire of seeing him then he kills his boss and confesses to that, too. The police don’t believe him, thinks he is crazy. His fiancé, who he loves, gets accused of the murder and now he can’t convince anyone he is the real murderer.