Tobruk, North Africa, 1942. Captain Anson, a battle-weary English Officer, is heading towards an alcohol-fuelled nervous breakdown. He is ordered, along with his loyal Sergeant Major, Tom Pugh, to escort two nurses, Sister Diana Murdoch and Sister Denise Norton, to Alexandria. The nurses have been separated from their unit during bombardment and now need to leave Tobruk as soon as possible before the city is besieged by the advancing German troops. The four of them set out on their journey in a rickety old army ambulance named Katy. Denise becomes hysterical and has to be sedated. Tom and Diana agree to keep Anson away from alcohol for the duration of the journey.

They encounter a lone South African soldier, Van der Poel, who they agree to take with them. Soon afterwards, they have to navigate a path through a minefield. Anson and Van der Poel argue about the best way to do this. The group then come across German tanks. Anson tries to outpace them, despite the fact that the Germans have opened fire. Eventually he stops, but it is too late: Denise has been shot. Rather than taking them prisoner, the Germans allow the group to proceed because they have a passenger who needs medical help: the fact that Denise is mortally wounded is concealed from them for fear of jeopardising their escape. Anson feels guilty and resolves to get all the remaining members of the group safely back to Alexandria where he will buy them an ice cold beer at his favourite bar. The next morning, they bury Denise's body, but the makeshift funeral is interrupted by the arrival of more German troops. Van der Poel is able to persuade the Germans to let them continue, thus arousing the suspicion of the other group members. Not only can he communicate effectively with the enemy, but he keeps disappearing off into the desert, accompanied by his heavy backpack with its mysterious contents, and, crucially, he doesn't know how to make tea the British way. However, he shows great bravery and Herculean strength when he supports the weight of the entire truck on his back during vital repairs.

The group has to change its planned route after discovering that German military advances have made it impossible. To make matters worse, Katy is becoming increasingly dilapidated. After stopping off at an oasis to pick up supplies, the party heads off towards the only route available: a perilous track through the depression, a boggy salt marsh whose surface can be as treacherous as quicksand. When Van der Poel disappears again with his pack that evening, Tom turns the truck's headlights onto him. It is as they had suspected: his pack contains a radio transmitter. He is a German spy. Despite this discovery, when he gets into serious difficulties in the boggy marsh and is being sucked under, the rest of the group rescue him.

The group has almost reached its destination, and Diana makes a pass at Anson, of whom she has grown increasingly fond. The couple enjoy a brief embrace in the sand. The next morning, the group faces its last challenge: a steep sandy slope that it is impossible to drive up. Tom hits upon the idea of using the starter handle to crank Katy painstakingly backwards up the incline. It works, and all spend several hours slowly advancing the truck up the hill, inch by inch. They are almost at the top when disaster strikes: Diana lets go of the handle momentarily and the truck rolls unstoppably back down the hill. Everyone is distraught, but they repeat the process and eventually reach the top. On the final leg of the journey, Anson, Tom and Diana realise that they do not want Van der Poel, who has played an important part in their group survival, to be shot as an enemy spy. When they finally reach Alexandria, they have the long-awaited beer together. Van der Poel is forced to admit that he is actually Hauptmann Otto Lutz so that Anson and the others can pretend that they have known his true identity all along. The military police take Otto away to a prison camp.