"Damn the Defiant." a 1962 film directed by Lewis Gilbert, is based on an actual incident, known as the Spithead Mutiny which took place during the 1797 war with France.
The ship is led by Captain Crawford (Alec Guinness), a fair man who is afraid to rattle the cage of his next in command, the sadistic Lieutenant Scott-Padget (Dirk Bogarde), who is well-connected and has ruined the careers of previous captains. The ambitious Scott-Padget, however, is determined to take over the ship and wants things his way. To this end, he brutalizes Crawford's young son, who is on board as a midshipman, knowing that the principled Crawford will not interfere.
However, there are mutineers on board, led by Vizard (Anthony Quayle) who have written a petition for better food and more money. They hate Scott-Padget, and if they take control, he's in big trouble.
This is a very good film with suspense as well as excitement, dominated by the acting of Guinness and Bogarde. Guinness is brilliant - you can see him making an effort to control his anger, and one also sees his great pain. When he at last asserts himself, he is very noble. Director Gilbert had to fight for Bogarde, so devalued was he by Hollywood, but Guinness spoke up for the actor as well, and he was cast. He does a great job - handsome, outwardly polite, and mean as dirt. Anthony Quayle is excellent as Vizard, who, in leading his men, demands patience.
Absorbing and entertaining, even if movies on the high seas aren't your thing.