Glover was a professional wrestler for many years, going under the ring name "Leon Arras the Man From Paris", and latterly worked as a school teacher (teaching English and French). His first acting job came playing Mr. Sugden, the comically overbearing sports teacher in Ken Loach's film Kes (a job he got when the film's writer, a teaching colleague, suggested him to the director).

An untrained actor, Glover proved to be a skilled and flexible character actor. While his trademark bald head, stocky build, and gruff Yorkshire accent garnered him many roles as tough guys and criminals, he also played Bottom in A Midsummer Night's Dream, had a recurring role in the classic sitcom Porridge, played Quilp in The Old Curiosity Shop, and lent his voice to a number of animated characters, including one of the "Tetley Tea People" in a long-running series of television advertisements. He also appeared in An American Werewolf in London, Alien³, and Leon the Pig Farmer. His stage career included a stint with Britain's Royal National Theatre (appearing in Saint Joan and Don Quixote), performances of The Canterbury Tales, and led him to a number of roles in TV plays, shown as part of the Play for Today series. Glover played Lugg, the endearing rogue manservant to Albert Campion in the TV series Campion. He also took a role in the Doctor Who story Attack of the Cybermen in 1985.

"You play to your strengths in this game. My strength is as a bald-headed, rough-looking Yorkshireman" Brian Glover once said

He was married to Tara Glover. Latterly a sufferer from a brain tumor, Brian Glover died in a London hospital in 1997.