The ocean liner SS Britannic is in the middle of a voyage in the North Atlantic with 1200 passengers on board when the shipping line’s owner Nicholas Porter in London receives a telephone call from an unidentified person with an Irish accent styling himself as “Juggernaut”, who claims to have placed seven drums of high explosives aboard the ship which are timed to explode and sink it at dawn on the following day. He warns that the drums are booby-trapped in various ways and that any attempt to move them will result in detonation, and offers that technical instructions in how to render the bombs safe will be given in exchange for a ransom of £500,000. As an indication of his seriousness he then sets off a demonstration attack with a series of small bombs behind the ships funnel, which injure one crewman. Unable to order an evacuation of the ship’s passengers via lifeboats due to rough seas, the shipping line’s management is inclined to yield to the ransom demand, however British government officials inform the company that if it does so they will withdraw the company’s operating subsidy in line with the Government’s policy of non-appeasement of terrorism.

Instead, a Royal Navy officer, Lt. Cmdr. Anthony Fallon, leading a bomb-disposal unit, is dispatched, arriving on the scene by air transit and parachuting into the sea, to board the ship and defuse the barrel-bombs before the deadline. Meanwhile, back in London, Supt. McCleod, whose wife and two children happen to be holidaying on board the ship, leads Scotland Yard’s investigation against the clock to capture the criminal master-bomber.

After an attempt to drill a hole into one of the barrel-bombs fails, setting it off and damaging the ship, Fallon decides to split up his team with each man working simultaneously on each of the remaining devices at different points around the ship, Fallon going first with each stage of the defusing operation and informing his men of each move by radio link, with the aim that if he fails and his bomb explodes, his men will know what went wrong and continue the process onwards, with his second in command taking up the lead, until the devices are disarmed. However, if two more bombs go off, the ship will sink. Fallon proceeds to disarm the bomb he is working on, apparently successfully, with his men following each step. However, it contains a hidden secondary mechanism and one of his men, close friend Charlie Braddock, accidentally triggers it, resulting in his death when it explodes, causing further damage to the ship. A distraught Fallon abandons the operation and tells the ship’s captain, Alex Brunel, to advise the shipping line to pay the ransom to avoid any more carnage. However, when negotiations with Juggernaut break down (in part because Juggernaut sees the trap police set for him when he goes to collect the ransom) Fallon is ordered by the captain to continue disarming the remaining bombs.

Meanwhile, an extensive police search back in London captures the bomber posing as Juggernaut, who is revealed to be an embittered former British military bomb-disposal officer, Sidney Buckland. He is escorted to the police situation room. After a brief interrogation he agrees to tell Fallon—whom he knows personally, having trained him as a junior officer—how to disarm the bombs. Time is running out and the dawn detonation is fast approaching. Fallon and Juggernaut have a brief conversation, and, because of their former comradeship, Juggernaut agrees to tell Fallon how to safely disarm the bombs. Juggernaut gives the instruction. Fallon, somehow sensing he is being misled, does the opposite of what he is told, and in so doing is successful in disabling the bomb. The rest of the bomb-disposal unit swiftly follow Fallon’s example, and the ship and its passengers are saved.