At age nine, he and his family (brother Elliot and sister Debra Lynne) moved to Valley Stream, New York where he attended Memorial Junior High and then Valley Stream Central High School.
Brandon starred in the television series Dempsey and Makepeace and Dinotopia, the movies Quattro mosche di velluto grigio (1971), Field-Marshal (1978), A Vacation In Hell (1979) and A Change of Seasons (1980), and the plays Does a Tiger Wear a Necktie? and Jerry Springer - The Opera. Since moving to the United Kingdom, Brandon has worked in television on such shows as The Bill, Trial and Retribution, and Dead Manitoba Weds. He also played the title role in the musical Jerry Springer: The Opera for over a year in the National Theatre and after its transfer into the West End.
Brandon starred in Singin" in the Rain in the summer of 2012.
In February 2008 he began his talk radio show on City Talk, a new local radio station in Liverpool. In 2008 he appeared in the Series 4 finale of the British Broadcasting Corporation"s Doctor Who, as General Sanchez, a UNIT officer
Also in 2008 he appeared in the television series Bones, as Roger Frampton, an American millionaire. In the early 1970s Brandon was in a relationship with the actress Kim Novak.
From 1976 to 1979, Brandon was married to actress Lindsay Wagner.
Brandon and Barber have a son, Alexander Max Brandon, born November 1992. In 2011, Brandon guest-starred in an episode of the BBC1 con drama Hustle as Marcus Wendell (series 7, episode 3). Also in 2011 he was seen in a supporting role in the film Captain America: The First Avenger as a politician who befriends the titular character.
In September 2013 he appeared in the Independent Television dancing show Stepping Out with wife Glynis Barber.