Born in Oxford, Oxfordshire, England, Angel made her first film appearance with a leading role in Night in Montmartre (1931), and followed this success with The Hound of the Baskervilles (1932). Over the next few years she played strong roles in such films asThe Mystery of Edwin Drood (1935), The Three Musketeers (1935), The Informer (1935), The Last of the Mohicans (1936) and The Bold Caballero. In 1937 she made her first appearance in the popular Bulldog Drummond series, in a role she would eventually play in five films.
She was cast in such prestigious films as Pride and Prejudice (1940), Kitty Foyle (1940), That Hamilton Woman (1941), and two Alfred Hitchcock films, Suspicion (1941) and Lifeboat (1944). Her film appearances in the following years were few, but she returned to Hollywood to provide voices for the Walt Disney animated films Alice in Wonderland (1951) and Peter Pan (1953). She also played a continuing role in the television soap opera Peyton Place from 1964 until 1965.
Angel was married to Robert B. Sinclair, a television director. On January 4, 1970, an intruder broke into their home; when Sinclair attempted to protect Angel, the intruder killed Sinclair in Angel's presence, then fled. The incident is believed to have been a failed burglary. She died from cancer in Santa Barbara, California, and currently has a star on the Hollywood Walk of Fame, for her contributions to Motion Pictures, at 6312 Hollywood Boulevard.