In 1797, the humane Captain Crawford (Guinness) is in command of the warship HMS Defiant during the French Revolutionary Wars. He soon finds himself in a battle of wills with his first officer, the sadistic and supercilious first lieutenant, Mr. Scott-Padget (Bogarde). The Lieutenant believes that Crawford is too soft on his crew, and also disagrees with the captain's decision to proceed with orders to sail to Corsica despite word that Napoleon has overrun much of Italy. Scott-Padget has powerful family connections, which he has used in the past to "beach" two previous commanding officers with whom he disagreed. Knowing that Crawford is helpless to intervene, Scott-Padget subjects the former's son, Midshipman Harvey Crawford (David Robinson), to excessive daily punishments so as to gain leverage over the captain.
Meanwhile, some of the crew, led by seaman Vizard (Anthony Quayle), are organising to strike for better conditions, in conjunction with similar efforts throughout the British fleet. They eventually pledge virtually the entire crew.
In the Mediterranean, the Defiant encounters a French frigate escorting a merchant ship. After a sharp engagement, a boarding party from the Defiant captures the French frigate, and the merchantman surrenders. Crawford dispatches his son as part of the prize crew tasked to send the captured merchantman back to a British port, thereby placing him out of Scott-Padget's reach. Crawford tells Scott-Padget that bringing his son with him was a mistake, but now he's "put it right!" He further vows to take actions that will 'astound' his second-in-command. Before long, Scott-Padget is confined to quarters as punishment for insubordination. His humiliation is compounded by the requirement that he appear on deck every two hours in full dress uniform; a punishment usually reserved for young midshipmen.
Soon, Defiant fights and captures a Venetian frigate, taking on many prisoners. Crawford is severely wounded in the action and eventually loses his arm. Discovered among the prisoners is a key aide to Napoleon, from whom the British learn important information about a planned invasion of Britain.
With Crawford temporarily out of the way, Scott-Padget takes command, but his brutality goads the crew into a premature mutiny. Appealing to their patriotism, Crawford convinces Vizard and the other mutineers to sail for the main British fleet blockading Rochefort to warn them of the impending invasion. Crawford promises to intercede for the crew as best he can, on the condition that none of the officers are harmed.
As the Defiant reaches the fleet at Rochefort, they receive word that the main British fleet has already gone on strike, with the naval high command agreeing to most of the sailors' demands. The crew's jubilation at the news is cut short when the hot-headed seaman Evans murders Scott-Padget. Realising that they are now all doomed to punishment as mutineers, an enraged Vizard kills Evans. Their only course now is to try to escape with the ship.
Just then, the French fleet sallies out from port, and a French fireship is sighted heading straight for the British flagship. As the only ship under sail, the Defiant has the unique opportunity to save the flagship. Once again, Crawford appeals to the crew's patriotism, convincing them to intercept the fireship and promising pardons to all who fight. Vizard is killed in the ensuing action, living just long enough to hear a message from the British admiral thanking Defiant for their gallant actions.