Martin was born in Romford, Essex.
She made her Broadway debut opposite Julie Andrews in The Boy Friend in 1954. Her additional New York theatre credits include taking over as Dorothy Brock in the original Broadway production of 42nd Street and performing the revue Side by Side by Sondheim with Julia McKenzie and David Kernan, for which she was nominated for the Tony Award for Best Featued Actress in a Musical. She received a second Tony nomination for the musical King of Hearts.
In London, Martin starred with Paul Scofield and James Kenney in Expresso Bongo at the Saville Theatre. In 1959, she had also appeared in The Crooked Mile. Also in West End, she starred opposite Jim Dale in The Card in 1975.
In 1988 Martin joined the London production of the Sondheim musical Follies, starring with Eartha Kitt.
More recently, in 2008 she appeared at the Open Air Theatre, Regent's Park with Topol, Linda Thorson and Lisa O'Hare in the Lerner & Lowe musical, Gigi.
During the early 1960s, Martin became known to British television audiences as the resident singer of topical songs on the original British version of the weekly satire show That Was The Week That Was (1962–63). One of the songs she sang on the show, the John F. Kennedy tribute "In the Summer of His Years", was released as a single and 'bubbled under' the Billboard Hot 100 chart at No 104 in 1963 (but was outcharted by a cover version by Connie Francis, which reached No 46). She has also released recordings in Swedish, such as the 7" single "Om du nånsin skulle ändra dej".
Martin had her own BBC television series between 1964 and 1966, titled Mainly Millicent for the first two series, and shortened to Millicent for the third and final series. In one episode, Martin and guest star Roger Moore performed a comedy skit in which Moore played secret agent James Bond some years before he was cast in the role. In the mid-1960s she guested, alongside Pete Murray and Kenneth Williams, in an edition of Juke Box Jury. She also appeared in the 1966 film Alfie starring Michael Caine.
In 1969, Sir Lew Grade wanted to make a comedy film series, starring Martin, that would appeal to both American and British audiences. He sent six comedy sketches of Martin to producer Sheldon Leonard, who came up with the premise of From a Bird's Eye View. The series was not a success and was cancelled after 16 episodes had been filmed.
In 1977, on Jubilee Day, she appeared in a gala edition of BBC TV's The Good Old Days to celebrate the Queen's Silver Jubilee, performing in a double act with Julia McKenzie.
Martin appeared as Gladys Moon in 13 episodes of Moon and Son, a 1992 BBC detective series created by Robert Banks Stewart, and co-starring John Michie.
In 2005 she had a small part in the film, Mrs. Palfrey at the Claremont which starred Joan Plowright.
Her later television roles include Gertrude Moon, Daphne Moon's Mancunian mother, in the American sitcom Frasier. She has worked for the Disney Channel, starring in the shows The Suite Life of Zack & Cody, Jonas and in the film Return to Halloweentown. Other performances include guest roles in The Drew Carey Show, Will & Grace and Days of Our Lives. She also had a small role on an episode of Gilmore Girls and a key role in an episode of "Modern Family".
In 2011 she guest-starred opposite her former Frasier daughter, Jane Leeves, in the TV Land series Hot in Cleveland. She has also had an appearance in the fourth season of Chuck as the mother of Hartley Winterbottom, who was given the first Intersect prototype and became Alexei Volkoff; she also guest-starred on an episode of the fourth season of Castle as a theatre critic who wrote a harsh review of a performance given by Castle's mother.
Martin was married to the pop singer Ronnie Carroll from 1958 until 1965, and subsequently to actor Norman Eshley, but both marriages ended in divorce. She has been married to American Marc Alexander since 1978 and is now a permanent resident of the United States.