A series of mysterious and dangerous incidents begin to plague the development of the world's first supersonic airliner, the SST1. These accidents range from a man being murdered by a homicidal air stewardess to sabotage acts carried out by two women during crucial testing phases. In response, the Air Ministry enlists Hugh "Bulldog" Drummond, played by Richard Johnson, to investigate the escalating threats and uncover the culprit behind these sabotage attempts.
Accompanied by the rather naive and bubbly American named Flicky, portrayed by Sydne Rome, Drummond soon discovers that a criminal genius, Carl Petersen, is behind the chaos. Petersen, who stands to gain a hefty eight million pounds if his plans succeed, has devised a sinister scheme involving highly advanced robots—attractive women equipped with electronic brains. These robots are being used to secretly sabotage the SST1 project by employing infrasound technology, which produces sound waves below the threshold of human hearing but can cause severe damage when directed at people or machinery.
The robot-assisted sabotage begins with attacks on the aircraft, but Petersen's plans quickly turn deadly as Helga (played by Daliah Lavi) and Pandora—more lethal and intelligent female robots—start to systematically eliminate key individuals involved in the project. Among those targeted are Dudley Mortimer (a character played by Maurice Denham), an engineer, and the secret agent Miss Mary (who runs a cooking class as a cover for her espionage activities). Helga, showing both allure and menace, even attempts to kill Drummond by planting a bomb in his telephone after sleeping with him during a chance encounter at a shooting party. She also tries to crash his glider in an effort to eliminate him. Fortunately, Drummond manages to manually open his parachute after the ripcord is sabotaged and escapes death in a tense, life-threatening moment.
The investigation then takes Drummond to North Africa, where he follows up on a lead related to an infrasound-powered powerboat. Here, he receives assistance from Peregrine Carruthers (played by [Ronnie Stevens]), a contact at the British Embassy. Pandora also attempts to steal the powerboat using a miniature infrasound device, and in a thrilling race, Drummond and Peregrine compete against Helga and Pandora, who manage to capture the men and the vessel. The villains deliver them all to Petersen’s island hideout, which is manned by a host of female robots, including the endearing but malfunctioning No. 7.
On the island, Drummond reunites with Flicky, who has successfully infiltrated Petersen's organization. During a dinner, Petersen reveals his devastating plan to use infrasound technology to destroy the SST1 during its maiden flight. That night, Drummond develops a closer relationship with Helga, after sleeping with her again, while Pandora seduces Peregrine, highlighting the manipulative nature of Petersen’s robotic creations. The following morning, Drummond attempts to retrieve the infrasound device but is intercepted. Flicky reveals that she is actually a double agent working for the Russians, and as she tries to escape with the device, Helga captures her at gunpoint. Drummond manages to escape but is eventually cornered by No. 7, who surprisingly chooses not to betray him, implying she is not truly a robot after all.
Petersen’s plan is set in motion as he forces Flicky—who is now a hostage— and Peregrine to witness the impending destruction of the SST1. Drummond, showing quick thinking and resourcefulness, scales the enemy’s fortress and uses Petersen’s own infrasound waves against him, effectively destroying the control room and thwarting the sabotage. Petersen, Pandora, and Helga are all presumed killed in the explosion, which saves the aircraft and the project.
In the aftermath, Drummond, Flicky, Peregrine, and the robot No. 7 escape the chaos. Flicky reveals her true allegiance as she escapes on the powerboat with the infrasound device, now in her possession. It is also inferred that Flicky is a double agent, working for the Russians, and she departs with the device, leaving Peregrine behind, who chooses to stay in order to foster better relations with Russia. As the island explodes in flames, Drummond finds solace in the company of No. 7, who turns out not to be a robot after all but a genuine, kind-hearted individual, adding a touch of unexpected tenderness to the high-stakes adventure.
