Born as Madeleine Angela Clinton-Baddeley in West Ham, Essex in 1904 into a wealthy family, she would later base the character of Mrs. Bridges on one of the cooks her family employed. Her younger sister was Actress Hermione Baddeley (1906–1986), who is known to American audiences for such appearances as on NBC's Little House on the Prairie.

In 1912, aged 8, Angela made her stage début at the Dalston Palace of Varieties, Dalston, in a play called The Dawn of Happiness. When she was nine, she auditioned at the Old Vic Theatre. In November 1915 she made her stage début at the Old Vic in Richard III, and she subsequently appeared in many other Shakespeare plays.

During her teenage years, the "consummate little actress", as a national paper had once called her when she was 10, starred in many musicals and pantomimes. She briefly 'retired' from acting at age 18. Her first marriage, to Stephen Thomas, produced one daughter. On 8 July 1929 she married actor/stage Director Glen Byam Shaw; they had two children, a son and a daughter.

After spending some time touring in Australia, Baddeley established herself as a popular stage Actress. At the beginning of the 1930s she appeared in two films, the Sherlock Holmes tale, The Speckled Band (1931), featuring Raymond Massey as Sir Arthur Conan Doyle's sleuth, and in The Ghost Train (also 1931), a screen version of the successful stage thriller. Later in the decade, Baddeley had a role in the MGM-British film, The Citadel (1938), an adaptation of A. J. Cronin's novel directed by King Vidor. Throughout the 1940s, she played many strong female roles on stage, including Miss Prue in Love for Love and Nora in The Winslow Boy.

She played the bawd in Tony Richardson's production of Pericles, Prince of Tyre at the Shakespeare Memorial Theatre in 1958. She played Mistress Quickly in several episodes of the BBC Shakespeare history series An Age of Kings, performing with her sister Hermione as Doll Tearsheet. In the original version of Upstairs, Downstairs (1971–75) she played "Mrs Bridges", the resident cook at 165 Eaton Place, who, when the show ended, married the butler, "Angus Hudson". A possible spin-off was in the works featuring Mrs. Bridges' married life with Mr. Hudson and her long-time kitchen maid Ruby Finch, but she died before it was developed and filmed. Baddeley replaced Hermione Gingold in the second cast of the original London run of the musical A Little Night Music.

She was made a CBE in 1975 for "services to the theatre". She died at Grayshott Hall in 1976 from pneumonia at age 71, shortly after Upstairs, Downstairs ended its run. She is interred, along with her husband Glen Byam Shaw, at St Mary's Church, Wargrave, Berkshire.