In the early months of the Second World War, Nazi Germany's Kriegsmarine sends out merchant raiders to attack Allied shipping. The heavily armed German pocket battleship the Admiral Graf Spee sinks a British merchant vessel, the Africa Shell. The Africa Shell's crew is brought aboard the Admiral Graf Spee. The Admiral Graf Spee docks with its supply ship and more captured British seamen are brought aboard. Three weeks later, the Admiral Graf Spee sinks another British vessel, the Doric Star. Her crew is also brought aboard.

The Royal Navy responds with hunting groups whose mission is to stop these attacks on Allied shipping. The group that finds the Admiral Graf Spee near South America is outgunned since Admiral Graf Spee is equipped with long-range 11.14-inch (283 mm) guns, and the British heavy cruiser Exeter has much lighter 8-inch (203 mm) guns, and the light cruisers Ajax and Achilles have 6-inch (152 mm) guns. However, they go straight into the attack, closing swiftly to minimize the Graf Spee's substantial advantage in range of shot.

The British are led by Commodore Harwood (Anthony Quayle), with Captain Woodhouse (Ian Hunter) commanding flagship Ajax, Captain Bell (John Gregson) Exeter and Captain Parry (Jack Gwillim) Achilles. The British use their superior numbers to split her fire by attacking from different directions, but Admiral Graf Spee, under Captain Hans Langsdorff (Peter Finch), inflicts much damage on her foes. Exeter is particularly hard hit and is forced to retire from the battle.

Admiral Graf Spee sustains some damage and takes refuge in the neutral port of Montevideo, Uruguay, for repairs. According to international law, the ship may remain in a neutral harbor only long enough to repair for seaworthiness, not to refit for battle; any overstay will lead to the ship and its crew being interned for the duration of the war. The British initially demand the Uruguayan authorities send Admiral Graf Spee out to sea within 24 hours, but once they recognize that reinforcements can arrive for an impending second battle they change strategy and lobby for an extension for the Germans. In reality the most powerful British ships are still extremely distant, but local media spreads false reports that more Royal Navy warships have arrived, including battleships and aircraft carriers; in fact, only three cruisers (Exeter having been replaced by HMS Cumberland) lie in wait.

Taken in by the ruse, Langsdorff takes his ship out with a skeleton crew aboard. As the onlookers watch from shore, she heads down the River Plate for the open sea, bursts into flames from a series of explosions; they realise she has been scuttled. That is a relief to the Royal Navy fleet, which reports, "Many a life has been saved today". Later, aboard a German merchant ship in the inner harbor, Langsdorff is complimented for his humane decision by British merchant marine Captain Dove.