The film is set within Terminal 2 of London Heathrow airport during a fog. As flights are delayed, the VIPs (very important people) of the title play out the drama of their lives in a number of slightly interconnected stories. The delays have caused serious hardship for most of the characters and have plunged some of them into a deep personal or financial crisis.
The central story concerns famed actress Frances Andros trying to leave her husband, millionaire Paul Andros, and fly away with her lover Marc Champselle. Because of the fog, Andros has the opportunity to come to the airport to convince his wife not to leave him.
Film producer Max Buda needs to leave London, taking his newest protégée Gloria Gritti with him, by midnight if he is to avoid paying a hefty tax bill. The Duchess of Brighton, meanwhile, is on her way to Florida to take a job which will pay her enough money to save her historic home.