At the age of sixteen, Court met film Director Anthony Asquith in London; the meeting won her a brief part in Champagne Charlie (1944). Court won a British Critics Award for her role as a crippled girl in Carnival (1946) and also appeared in Holiday Camp (1947) and Bond Street (1948). Her first role in a fantasy film was in Ghost Ship (1952). One of Court's most remembered films is the cult classic Devil Girl from Mars (1954). She trained at the Rank Organisation's "charm school".

Court was married to Irish actor Dermot Walsh from 1949 until their divorce in 1963. They had a daughter, Sally Walsh, who appeared with her mother in The Curse of Frankenstein.

In the 1957–58 television season, she co-starred in a CBS sitcom filmed in England, Dick and the Duchess, in the role of Jane Starrett, a patrician Englishwoman married to an American insurance claims investigator living in London, a role played by Patrick O'Neal. Court travelled back and forth between Hollywood and England, appearing in four episodes of Alfred Hitchcock Presents. She had parts in A Woman of Mystery (1958), The Man Who Could Cheat Death (1959) and Doctor Blood's Coffin (1961) among others.

By the early 1960s, Court had permanently moved to the United States. She was featured in the Edgar Allan Poe horror films The Premature Burial (1962), The Raven (1963) and The Masque of the Red Death (1964), the last two with Vincent Price. She appeared on occasion in the popular early 1960s TV series (each episode a stand-alone drama), the Dick Powell Theatre.

From 1964 until his death in 1998, she was married to American actor Don Taylor, who was divorced in 1955 from Actress Phyllis Avery. Court retired from the film acting Business in 1964 to concentrate on being a wife and mother. Court and Taylor met while they were shooting an episode of Alfred Hitchcock Presents. They had a son, Jonathan, and a daughter, Courtney.

In 1981 Court appeared briefly in the third Omen film, The Final Conflict, although she was uncredited. She also appeared in episodes of several TV series, including Adventures in Paradise, Mission: Impossible, Bonanza, Dr. Kildare, Danger Man, Twelve O'Clock High, Burke's Law, Sam Benedict, Gidget, McMillan and Wife, Mannix, The Wild Wild West, Thriller, and in "The Fear", the penultimate episode of the original 1960's The Twilight Zone.

Court died of a heart attack at her home near Lake Tahoe, California, on 15 April 2008, aged 82. She was survived by daughters Sally Walsh and Courtney Taylor, son Jonathon Taylor and two stepdaughters, Anne Taylor Fleming and Avery Taylor. She was cremated and her ashes were scattered at sea. Hazel Court once said in an interview "Just in case I should pop off to heaven in the night, I always remember to wash up, plump-up the cushions and straighten up after a dinner party. I wouldn't want everyone to come in and find it a mess. It's very English of me."

In addition to acting, she was also a Painter and sculptress, and studied sculpting in Italy. Court wrote her autobiography, Hazel Court – Horror Queen, which was published by Tomahawk Press in the UK (April 2008) and in the US (June 2008).