Born in Nottingham, he first trained as an actor at the Guildhall School of Music and Drama and also appeared in ITV Television Playhouse and The Wednesday Play before moving full time into writing in the late 1960s. In this role, he wrote for Half Hour Story, The Company of Five, The Wednesday Play, Play For Today, Suspicion, Thirty-Minute Theatre, Plays for Britain and Play for Today before producing his best known work, Scum, for the latter strand in 1977. It was banned by incoming BBC1 Controller Bill Cotton. Undeterred, Minton and director Alan Clarke made a cinema version which was released to great acclaim but, again, controversy.
He went on to write the film Scrubbers but changes were made to the screenplay without his knowledge. He disassociated himself from the film and instead turned to play and novel writing.