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. He has been married to Actress Glynis Barber, with whom he co-starred in Dempsey & Makepeace, since 1989. They remain in the United Kingdom. Together, Brandon and Barber have a son, Alex.

Brandon starred in the TV series Dempsey and Makepeace and Dinotopia, the movies Quattro mosche di velluto grigio (1971), F.M. (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 UK, Brandon has worked in TV on such shows as The Bill, Trial and Retribution, and Dead Man 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 2004, he portrayed Nobel Prize winner Arno Penzias in the BBC TV movie Hawking about Physicist Stephen Hawking's early career at the University of Cambridge and was the US narrator of Thomas & Friends. 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 BBC'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.

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 ITV dancing show Stepping Out with wife Glynis Barber.