A Polish theater company in Warsaw is preparing to stage an anti-Nazi melodrama on the eve of World War II. Maria and Joseph Tura, who specialize in performing Shakespeare, are rehearsing for the leading roles. However, the Polish government cancels the production out of fear that the performance of a play critical of the Nazi regime will worsen relations between Berlin and Warsaw. The actors instead present a performance of "Hamlet", with Maria and Joseph in the title roles.
During the performance, Lieutenant Sobinski, a pilot in the Polish Air Force, visits Maria backstage. These meetings come to an end when war breaks out and Sobinski flees to London, while the Turas remain in Warsaw.
In London, Professor Siletsky, a Nazi agent posing as a Polish patriot, tells Sobinski and a group of Polish freedom fighters serving in the British Air Force that he is returning to Warsaw on a secret mission. Gaining their trust, Siletsky obtains the names and addresses of their friends and relatives in Warsaw, including Maria Tura, whom Sobinski refers to as "Poland's leading actress" but who is unknown to Siletsky. Sobinski reports his suspicions about Siletsky to British military intelligence and is sent to Warsaw with instructions to recover the list of names and addresses.
In Warsaw, Sobinski is aided by Maria and the theater troupe in his mission. Siletsky, meanwhile, orders Maria's arrest and brings her to his suite at the Hotel Europejski, where he tries to win her over to the Nazi cause. The actors, disguised as Nazi soldiers, take Siletsky to the theater where he is confronted by Joseph Tura, who is disguised as a Gestapo chief. After learning the location of the list of names, Tura delays the interview, causing Siletsky to grow suspicious. Siletsky escapes into the auditorium and is shot by Joseph.
To rescue Maria and secure the list of names, Joseph disguises himself as Siletsky and returns to the hotel. He is later arrested and brought to the office of the real Gestapo chief, Colonel Ehrhardt. As Ehrhardt prepares to reveal Joseph's disguise, the actors, still in Nazi uniforms, burst into the office and "arrest" Joseph.
The theater troupe, including Sobinski, disguises themselves as high-ranking Nazis in order to escape from Warsaw. With one actor impersonating Hitler, they steal a car and fly to the British Isles.