Mower was born in Oxford to a Welsh father and English mother. In his 2007 autobiography, Mower states that having believed for years that his year of birth was 1940, but later discovered that his birth was not registered and he was born on 12 September 1938. In addition, several reference books on film and television, including Who's Who On the Screen (1983) and Who's Who on Television (1996), give Mower's town of birth as Pontypridd, South Wales, instead of Oxford. For seven years Mower was the partner of the actress Suzanne Danielle.