Tobruk, a British base, is attacked by the German Afrika Korps in the Western Desert Campaign of World War II.  During the resulting evacuation, MSM Tom Pugh (Harry Andrews) and nurses Diana Murdoch (Sylvia Syms) and Denise Norton (Diane Clare) — the crew of anAustin K2 ambulance, which was named 'Katy' by its original driver — become separated from their unit and are forced to flee cross-country. With them are Captain Anson (John Mills), suffering from battle fatigue and almost an alcoholic, and an Afrikaans-speaking South Africanofficer Captain van der Poel (Anthony Quayle), who carries a large pack he seems very attached to. Anson motivates himself by thinking of the ice cold lager he will order when they finally reach the safety of Alexandria, Egypt — the 'Alex' of the title.  En route, the group meets with various obstacles including a minefield, a broken suspension spring (during its replacement, van der Poel's great strength saves the group when he supports 'Katy' when the jack collapses), and the dangerous terrain of the Qattara Depression. Twice the group encounters parties of Afrika Korps soldiers; in one encounter they are fired upon, and Norton is fatally wounded. Van der Poel, who speaks German, is able to talk the Germans into allowing them to go on their way.  The second time, however, they seem reluctant, until he shows them the contents of his pack.