Rimmer appeared mainly in supporting roles, especially in films and television series produced in the United Kingdom. He emigrated to England in 1959, after initially performing as a cabaret singer.

Rimmer married Sheila Logan in 1963. They had three sons, Damien, Ben and Paul.

Rimmer appeared once in Doctor Who (in the 1966 serial The Gunfighters), and twice in Coronation Street: as Joe Donnelli (from 1968 to 1970), who held Stan Ogden hostage before taking his own life, and Malcolm Reid (in 1988), the adoptive father of Audrey Roberts’ son Stephen. He made many guest appearances in British TV series for ITV, including Roald Dahl’s Tales of the Unexpected, as well as ITC’s The Persuaders! In 1980, Rimmer played Edward Condon in the BBC mini-series Oppenheimer, which was rebroadcast in the United States in 1982, and appeared in the 1984 miniseries Master of the Game, opposite Dyan Cannon.

In 1989, Rimmer was reunited with Bishop and Zimmerman during the production of a BBC Radio 4 adaptation of Sir Arthur Conan Doyle’s A Study in Scarlet. In 2012, he recorded a reading of Donald Cotton’s Doctor Who novelisation of The Gunfighters for release in February 2013.

Rimmer and American actor Ed Bishop—himself an Anderson associate–would joke about how their professional paths frequently crossed, calling themselves “Rent-a-Yanks”. They appeared together as United States Navy sailors in The Bedford Incident (1965) and as NASA technicians in the opening of You Only Live Twice (1967), as well as touring together on stage, including a production of Death of a Salesman in the 1990s. Rimmer and Bishop also appeared in the BBC drama-documentary Hiroshima, which was completed shortly after Bishop’s death in 2005.

In 2010, Rimmer returned to the world of Thunderbirds with a 15-minute fan film simply entitled Thunderbirds 2010. He portrays Jeff Tracy in a voiceover on Thunderbird 3’s radio, towards the end of the movie, instructing Scott and Alan to take the three astronauts they rescued in the movie to an intact space station, and return to Tracy Island in anticipation of a storm in the Pacific.

Rimmer played the role of Leo Carlin in the 2013 audio drama The Mighty Carlins by award-winning Canadian playwright Collin Doyle. The recording was produced by Wireless Theatre Company.

In 2014, Rimmer released his first fiction novel Long Shot, through amazon.co.uk/com. This marked his second foray into publishing, having released his autobiography From Thunderbirds to Pterodactyls four years previously.

In 2015, he played the role of “Anderson” in the science fiction short DARKWAVE: Edge of the Storm; this was released for free online the following year.

He was the 2nd voice of Louie Watterson in the Cartoon Network series The Amazing World of Gumball from 2014 to 2018. The episode “The Ghouls” was his final role before his death in 2019.

Rimmer died at Barnet Hospital in London on 29 March 2019, aged 89. He was survived by his wife and sons.