Court was born in Sutton Coldfield, Birmingham. Her father was G.W. Court, a notable cricketer who played for Durham CCC. At the age of fourteen, she studied drama at the Birmingham Repertory Theatre and the Alexander Theatre, also in Birmingham. At the age of sixteen she met the director Anthony Asquith in London, which won her a brief part in the 1944 film Champagne Charlie.
Court won a British Critics Award for her role as a crippled girl in Carnival (1946). She also appeared in Holiday Camp (1947) and Bond Street (1948). Her first role in a fantasy film was in Ghost Ship (1952). She also appeared in the campy Devil Girl from Mars and Doctor Blood's Coffin.
Hazel Court wanted to act in comedy films, and from 1957 to 1958 she was in the TV comedy series Dick and the Duchess. But she continued to appear in horror movies. In 1957 she had a part in the film The Curse of Frankenstein, where she gained the status of a "cult siren", partly due to her display of cleavage. She travelled back and forth between Hollywood and England, appearing in four episodes of Alfred Hitchcock's TV series. She had parts in A Woman of Mystery (1958) and The Man Who Could Cheat Death (1959) among others.
By the early 1960s, Court had permanently moved to the United States. She was featured in the Edgar Allan Poe horror movies The Premature Burial (1962), The Raven (1963) and The Masque of the Red Death (1964), the last two with Vincent Price.
From 1964 until his death in 1998, she was married to American actor Don Taylor. She retired from the film acting business in 1964 to concentrate on being a wife and mother. They had met while shooting an Alfred Hitchcock Presents episode, and the couple had a son, Jonathan, and a daughter, Courtney.
In 1981 she appeared briefly in the third Omen film, The Final Conflict, although she was uncredited. She has also appeared in episodes of several TV series, including Mission: Impossible, Dr. Kildare, Twelve O'Clock High, and The Twilight Zone.
In addition to acting, she was also a painter and sculptor, and studied sculpting in Italy. Court wrote her autobiography, Hazel Court - Horror Queen, which was released in the UK in December 2007 and due to be published by Tomahawk Press in the US in 2008.
Court died of a heart attack at her home near Lake Tahoe, California on April 15, 2008, aged 82. She was survived by her three children, and two stepdaughters, Anne Taylor Fleming and Avery Taylor.