The height of the Second World War. German U-boats are waging a constant battle against Allied supply ships. One such ship, the Jason, has been sunk in the Western Approaches, an area of sea stretching across the North Atlantic. Some 20 men and their captain are crammed into a lifeboat being buffeted by gale-force winds. They have a small amount of food and a semaphore. One man, Rawson, has sustained a serious injury to his head. The captain decides that their only option is to raise the mast and sail for Ireland.

In New York, a convoy of merchant navy ships loaded with vital military equipment is being prepared. The captains are called to a conference where they are advised against showing too much smoke at sea. The captain of the Leander complains that a sluggish speed will be difficult for him to maintain but is informed that they must keep the pace at all times. They will be given an escort of destroyers and American fighter planes.

The convoy leaves the following morning. On board the Leander, Chief Rogers speaks to Petty Officer Griffith, who is keen to get home for the wedding anniversary that in previous years his duties have made him miss.

On the lifeboat, the radio operator keeps signalling on the semaphore. Food is now severely rationed. Notches are gouged on the mast to keep a tally of days at sea. The sailors hear a plane droning overhead but fail to capture its attention.

That night, the captain hears the faint vibration of U-boat engines. Rawson is delirious and has to be punched in order to be kept quiet.

The Leander is struggling to retain its place in the convoy when a storm hits. The slow pace of the fleet leaves this smaller ship in danger of being dragged off course by the waves. The Commodore allows it to pull ahead of the others as long as it rejoins them in the morning.

In England, the Navy operations room discovers a cordon of U-boats stretched across the mid-Atlantic. The convoy is ordered to veer south.

The semaphore message from the lifeboat is finally picked up - by the same U-boat that sunk the Jason. The German captain decides to lie in wait for whoever comes to the sailors' rescue.

A plane is sent to warn the Leander of the convoy's change of course. But just as the ship prepares to swing south, the radio operator picks up the lifeboat's distress call. The captain decides to go to their aid.

On the lifeboat, the semaphore's batteries run down. The men are exhausted and the water ration has to be cut. They have been at sea for 14 days. The youngest of the group clutches his St Christopher and suddenly his crewmate John spots smoke on the horizon.

They prepare to turn about when Rawson spots a periscope off the stern. The men ignore him but the captain advises caution and stops them signalling to the Leander. A furious argument breaks out, but eventually everyone agrees that they can't endanger the ship and that they should pretend to have seen a boat coming from the other direction.

The U-boat captain, anxious to unleash his last two torpedoes, is momentarily fooled. The sailors desperately try to alert the Leander by flashing the sunlight off some scrap metal and then by using an improvised semaphore made of oars and sails. But the U-boat captain has realised his mistake and fires on the rescuers.

The Leander turns too late and one torpedo strikes home. Griffith is caught in the blast and trapped in the hold. The captain orders most of the men to abandon ship and retains a skeleton crew on board.

The U-boat crew see their quarry take to the boats and decide to finish off the Leander with machine-gun fire.

Rogers finds Griffith and helps him up onto the deck. They spot the approaching periscope and creep undercover towards the ship's gun. Thinking the Leander to be deserted, the U-boat surfaces and opens fire. Griffith is shot, but Rogers manages to sink the submarine. The lifeboat draws up alongside and the sailors are welcomed aboard.