April 1942. British submarine HMS Sea Tiger returns to base after an uneventful tour of duty. Most of the crew are looking forward to their leave, particularly the captain, Lt. Freddie Taylor, who plans a string of dates with girlfriends, and the coxwain Dickie Dabbs, who is looking forward to the wedding of his sister Ethel to his crewmate Mike Corrigan. But Mike himself is getting cold feet, and tries unsuccessfully to replace a sick crew-member who had been scheduled to remain with the submarine.

Unpopular hydrophone operator Hobson receives a letter informing him that his wife wants a separation. Learning from neighbours that she and his son have moved in with her brother, Hobson turns up drunk at the brother's fish and chip shop and starts a fight. A policeman arrives at that moment to inform him that he and the rest of the crew have been recalled with immediate effect.

The news of the recall reaches Mike just before the wedding, and Ethel, spotting his ill-disguised relief at the enforced postponement, gives him back her engagement ring. Also attending the pre-wedding gathering is torpedo operator Tug Wilson, who has been vying with Dickie for the attentions of another guest, Gladys.

With the crew reconvened, Taylor explains that their new mission is to intercept and sink the German battleship Brandenburg, which is leaving Bremerhaven for the Baltic Sea. To reach Heligoland Bight within 48 hours, full speed must be maintained and travelling on the surface of the water is necessary. On the way, they capture some stranded German airmen waiting to be rescued from a buoy. But despite shooting down the buoy's aerial, they fail to prevent the Germans from sending the alert that there is a British submarine in the area. Catching sight of plans, the German prisoners realise the mission of the submarine is to sink the Brandenburg. Once they enter a mined area, one of the Germans panics and reveals that they had already seen the battleship, meaning that it is already well out of range.

Nonetheless, Taylor decides they will make their way around Denmark and attempt to find the Brandenburg in the Baltic. The journey is hazardous, since they must negotiate anti-submarine nets, and fuel and provisions start to run low, but they eventually find their target in a convoy and fire all torpedoes. They fail to avoid the retaliatory depth charges launched against them and damage to the water room must be swiftly repaired. Realising that the oil they are losing is leaving a trail on the surface, Taylor hatches a plan to fake the sinking of the submarine by jettisoning clothing and the corpse of one of the Germans, before tipping the stern of the submarine to the surface and diving. The manoeuvre fools the pursuing ships.

With the shortage of food and oil now critical, Taylor proposes putting the crew ashore a nearby Danish island and blowing the submarine up. However Hobson, familiar with the island and able to speak German, suggests that he alone goes ashore in German uniform to establish if there is fuel that may be stolen. Taylor assents. Reaching the port by dinghy, Hobson convinces the German officer on duty that he is a Luftwaffe airman who has been shot down. His signalling to the submarine is spotted, however, and the alarm is soon raised. The submarine comes into harbour and, aided by the sympathetic captain of a Danish ship, begins to refuel, while Hobson fends off the attacking Germans with a machine-gun. One of the crew is killed while assisting Hobson, but the rest make it safely back to the restocked submarine, after igniting the oil reserves on the dock.

In August, the Sea Tiger, believed lost after successfully sinking the Brandenburg, receives a heroes' welcome at base. Taylor starts planning a fresh round of romantic dates, Mike is greeted by a forgiving Ethel, and Gladys chooses Tug over Dickie. Hobson is reconciled with his wife and son, to whom he gives a wooden model of the Brandenburg that he has carved.