Landen was born at Margate. He made his television debut in 1959 as Pip, in an adaptation of Great Expectations, and made his film debut in 1962. He first became well known when he starred in the TV series Mickey Dunne, and The Spies during the 1960s. He also had a parallel career as a stage actor, including as Richard Dazzle in the RSC's 1970 production of London Assurance.
On radio, he appeared in the 1976 BBC Radio 4 adaptation of Jim Eldridge's novel Down Payment on Death as Art Gordo. He also portrayed Rupert Purvis in the 1982 production of Tom Stoppard's play The Dog it was that Died and played the urbane Ambassador McKenzie in four series of Flying the Flag.
In 1977 Landen starred in his own situation comedy, Devenish, playing a Basil Fawlty type character in a Reggie Perrin-type situation; designing board games. In 1980 he starred as 'Barty' in the television series Pig In The Middle, with Liza Goddard.
Dinsdale Landen died at his home in South Creake, Norfolk on 29 December, 2003 after becoming ill with pneumonia. He had been diagnosed with oral cancer several years before his death but the cancer was in remission. He was married to the actress Jennifer Daniel.