His roles in British television sitcoms include Jimmy Anderson in The Fall and Rise of Reginald Perrin (1976–79), Ben Parkinson in Butterflies (1978–1983) and Lionel Hardcastle in As Time Goes By (1992–2005).

His film appearances include A Fish Called Wanda (1988), The Madness of King George (1994), Mrs Brown (1997), Tomorrow Never Dies (1997) and Paddington (2014).

[4] He served as a corporal instructor in small arms and field training in the Royal Marines during his national service from 1946 to 1948, following which he briefly worked as an unpaid trainee assistant stage manager.

[2] In 1978, Palmer appeared as organized crimelord Simon Sinclair in London Weekend Television's hard-hitting police drama The Professionals, the episode entitled "Where the Jungle Ends."

Campaigns he was involved with include the 'Slam in the Lamb' ads for the Meat & Livestock Commission and the Audi commercials in which he was heard using the phrase "Vorsprung durch Technik".

[6] He narrated the documentary series Little England, and he continued to appear in productions written by Reggie Perrin creator David Nobbs, the last of these being the radio comedy The Maltby Collection broadcast from 2007.

[2][12][13][14] In the New Year's Honours List published 31 December 2004 he was appointed an Officer of the Order of the British Empire (OBE) for services to drama.