Brett was educated at Eton College and trained at the Central School of Speech and Drama. He played many classical roles on stage, including a huge amount of Shakespeare, and made his first film and television appearances in 1955. In 1958, he married the actress, Anna Massey (daughter of Raymond Massey), but they were divorced in 1962. Years later, they would appear together in the BBC's dramatization of Rebecca (1978) -- Brett playing the hero, Max de Winter, and Massey playing the sinister Mrs. Danvers.
In 1976 he married Joan Wilson, but she died in 1985, and he did not remarry.
From the early 1960s onwards, Brett was rarely off British television screens. He played leading roles in many classic serials, notably appearing as D'Artagnan in the 1966 adaptation of The Three Musketeers. Many of his appearances were in comedy roles, but usually with a classic edge (he appeared in several Noel Coward plays). He joked that he was rarely allowed into the 20th century and never into the present day.
Brett's film career was never as distinguished as his stage and small-screen careers. He played Freddie Eynsford-Hill in the 1964 film My Fair Lady, but his singing voice was dubbed. Brett could sing, however, as he proved when he played Danilo in The Merry Widow on television in 1968.
Although he appeared in so many films and was such a familiar face on television, Brett is now best remembered for portraying Sherlock Holmes in a long series of television films (from 1984 to 1994), based on the original stories by Arthur Conan Doyle. After taking on the role, he made few appearances out of character and is considered the Sherlock Holmes of the 1980s and 1990s, as Basil Rathbone had been before him from his 1940s films.