A former RAF squadron leader, Matt Denant goes to Hendley, England to visit an airfield run by Titch, a friend. An employee there named Rodgers asks if he would kindly make a large wager for him on a horse. Denant does, but when the horse loses, Rodgers makes a promise to repay him. While strolling through Hyde Park, a woman strikes up a conversation with Matt, only to be charged with unlawful soliciting by Penter, a detective. Matt intervenes on her behalf, but when the two men fight, Penter's head strikes a park bench. Matt is placed under arrest. He is then sentenced to three years in prison after Penter dies. Believing it an unjust punishment, Matt escapes. Inspector Harris of Scotland Yard is assigned to find him, while Matt takes refuge in the home of Sir James Winton, whose daughter Dora helps him hide. An aeroplane is left for Matt by his friend, enabling him to flee to France, but he is betrayed by Rodgers once it's learned the police are offering a reward. Matt's aeroplane is caught in a heavy fog and crashes. He survives and takes refuge in a farm. Dora finds him and professes her love, also persuading Matt that he must turn himself in to the law.
Film critic A.H. Weiler of the New York Times wrote a positive review of the film, "As the harried convict, Rex Harrison gives a restrained but persuasive portrait of a man beset not only by physical but moral tribulations... The pace of Escape, as set by director Joseph L. Mankiewicz, is, on occasion, slower than might be desired, and scenarist Philip Dunne's script is sometimes given to lengthy conversation. But these are minor flaws in an adult work, which unspectacularly and effectively does justice to a serious theme. Similarly, critic Craig Butler appreciated the film, writing, "Mankiewicz does a very good job of emphasizing the script's strong points, and he uses a number of interesting visual touches to keep things lively during discussions of morality and other weighty issues... For his part, Harrison is in top form, finding multiple levels to play in dialogue that could easily devolve into rants and providing the kind of solid performance that is crucial to anchoring a film of this type. Neither he nor Mankiewicz can overcome the limitations of the script to make Escape a classic, but they do make it fairly engrossing."