Lee trained at the Royal Albert Hall, then made her début with a bit part in His Lordship (1932), when she was 19. She played a number of minor, often uncredited, roles in films during the early 1930s. She gradually began to get more prominent roles in quota quickies, particularly those made for Paramount British. She became known for her roles in films set amongst the wealthy particularly in Chelsea Life (1933), in which she starred with Louis Hayward. The film was set in the artistic community of Chelsea.
On the strength of her performances in quota films, in 1934 Lee signed a contract with Gainsborough Pictures, which was the biggest British production company of the era. She played leading lady roles in a variety of different genres at Gainsborough including a comedy-thriller The Camels Are Coming, a drama The Passing of the Third Floor Back, a horror film The Man Who Changed His Mind and a war film OHMS. She appeared in the 1935 Jessie Matthews musical First a Girl as the aristocratic other woman. In 1937 she starred in one of the studio's large-budget productions, King Solomon's Mines.
She had met her first husband, the director Robert Stevenson while shooting The Camels are Coming on location in Egypt. During 1938 she took time off from acting to give birth to her first child. In 1939 she and her husband switched to Ealing Studios which was now being run by Michael Balcon the former head of Gainsborough. She played a nineteenth century Irish music hall performer who falls in love with an aristocrat in the comedy Young Man's Fancy (1939) and a journalist who helps the heroes thwart a foreign enemy's plot against Britain in The Four Just Men (1939).
Her final film in Britain was Return to Yesterday about a young repertory theatre actress who falls in love with a Hollywood star she meets while touring in a small seaside town. With the Second World War imminent, she and Stevenson then went to the United States. She remained supportive of the British war effort and in 1943 appeared alongside other British actors in Forever and a Day, which was made to raise money for British charities.
When she and her husband moved to Hollywood she became associated with John Ford, appearing in several of his films, notably How Green Was My Valley, Two Rode Together and Fort Apache. She co-starred with John Wayne and John Carroll in Flying Tigers (1942).