Graham Williams joined the BBC in 1966 and worked as a script editor for several years on series such as The View from Daniel Pike (1971), Sutherland's Law (1973), Barlow (1971) and Z Cars (1962).

In 1977 he was made producer of Doctor Who (1963). On taking over the series, Williams was ordered by BBC bosses to lighten the tone and reduce the violence and horror content following Philip Hinchcliffe's highly successful but controversial period producing the series. Williams duly did this, introducing more humour to take the place of the more violent and horrific material.

During his three seasons producing the series, Williams had to face budget cuts and regular industrial action. It was the late 1970s, a time of economic turmoil, and this had unfortunate consequences on the production of many Doctor Who (1963) serials. He also found the series' star, Tom Baker, increasingly difficult to work with. Tom Baker had been working on the series since 1974 and was well established as one of the biggest stars on BBC television. When Williams arrived, Baker's relationship with his co-star, Louise Jameson, was not good and this occasionally led to tensions. She left at the end of Williams' first season.

During Williams' second season, tensions arose between Baker and Williams regarding the direction of the series. Baker made it known that he wanted more input into the series, which would include the right to approve scripts, casting of actors and directors. Williams resisted this, leading to a dispute that eventually involved the BBC One Controller, Bill Cotton, the Head of Drama, Shaun Sutton, and the Head of BBC Serials, Graeme MacDonald. Fortunately, this dispute was settled amicably, with both men agreeing to continue the status quo. The second season also saw the introduction of a replacement for Louise Jameson, Mary Tamm, although she only lasted for this season.

Williams' third and final season was notable for the involvement of Douglas Adams, a young Cambridge University graduate whom Williams appointed as script editor on the series following his script for the previous season, Doctor Who: The Pirate Planet: Part One (1978). Adams had already gained acclaim for his radio series, The Hitchhiker's Guide to the Galaxy, which had been broadcast the previous year, and this season of Doctor Who (1963) was notable for containing much of Adams' trademark humour. The series also saw the introduction of Lalla Ward as Mary Tamm's replacement.

Williams left Doctor Who (1963) after producing three seasons in 1979. Despite the troubles, he had made his mark. His era saw the introduction of K-9, the robot dog, which became a popular hit, as well as the Black and White Guardians (characters that re-appeared several years later) and his second season in charge was based around an ambitious story arc called The Key to Time, something quite unprecedented in the history of the series.

His involvement with the series was not over, however. In 1984 he was commissioned to write a story for Doctor Who (1963) called "The Nightmare Fair". This was never made, but Williams was able to write a novel based on his story for the Target Doctor Who (1963) book range.

After producing Doctor Who (1963), Williams left the BBC but stayed in television to produce Tales of the Unexpected (1979) and Super Gran (1985).

By the end of the 1980s, Graham Williams had left television and ran a hotel in Devon. He died in 1990 from a shooting accident.