Glamorous assassin Irma Eckman (Elke Sommer), disguised as an air stewardess, kills oil tycoon Henry Keller (Dervis Ward) with a booby-trapped cigar aboard his private jet, parachuting away before the plane explodes. She is picked up by a speedboat driven by her partner in crime, the equally beautiful Penelope (Sylva Koscina). The villainous pair then murder David Wyngarde (John Stone (actor)), making it look like a spear fishing accident. Sir John Bledlow (Laurence Naismith), one of the directors of Phoenecian Oil, suspects that both deaths were the result of foul play; he had received an urgent message from Wyngarde that he needed to get in touch with Keller regarding a "matter of life and death". He asks Wyngarde's friend, Bulldog Drummond (Richard Johnson (actor)), to investigate.