The film follows an Irishman living in Newcastle upon Tyne, where he becomes embroiled in an American businessman's plot to acquire a prominent jazz club.

The film's title refers to blues guitarist and singer T-Bone Walker's signature song "Call It Stormy Monday (But Tuesday Is Just As Bad)".

In Newcastle upon Tyne, Irishman Brendan finds an ad for a janitorial position at the Key Club owned by Mr. Finney.

En route to his interview, Brendan stops at a local shopping mall, where he crosses paths with an American woman, Kate.

Brendan is sent by Finney to retrieve the Kraków Jazz Ensemble from the airport and bring them to the Royal Station Hotel.

When Kate subsequently asks for the night off at the restaurant, her boss fires her, and she responds by breaking several stacks of plates.

Worried that Cosmo will have them killed, Kate asks Brendan to return to the United States with her to her hometown in Minnesota, to which he agrees.

Kate drives Brendan's Jaguar to her apartment to retrieve her things, but is surprised there by Cosmo, who claims there are two plane tickets to Minneapolis waiting for her at Heathrow Airport.

Writer-director Figgis, who had spent much of his formative years in Newcastle, wrote the film with specific locations throughout the city in mind.

[1] When the project attracted financing from the U.S.-based Atlantic Releasing,[1] it was suggested that the film be recast with American actors, after which Melanie Griffith and Tommy Lee Jones were cast in the roles of Kate and Cosmo, respectively.