During the 1960s, Cribbins became known in the UK for his successful novelty records "The Hole in the Ground" and "Right Said Fred" and for his appearances in comedy films including Two-Way Stretch (1960) and the Carry On series.

His other screen roles include the astronaut Vincent Mountjoy in The Mouse on the Moon (1963), Albert Perks in The Railway Children (1970), the barman Felix Forsythe in Alfred Hitchcock's Frenzy (1972) and the pretentious hotel guest Mr Hutchinson in the Fawlty Towers episode "The Hotel Inspectors" (1975).

In 1960, he starred alongside Anna Quayle and Lionel Blair in the revue And Another Thing, written by Ted Dicks and Myles Rudge.

[11] Subsequently, Rudge and Dicks were asked to provide new material for Cribbins; their compositions "The Hole in the Ground", about an annoyed workman who eventually buries a harasser, and "Right Said Fred", about three workmen who struggle to move an unspecified heavy and awkward object into or out of a building (later also the name of a pop novelty band who named themselves after the song[12]), were top ten hits on the UK Singles Chart in 1962.

[1] His other appearances include the second Doctor Who film Daleks' Invasion Earth 2150 A.D. (1966) as Special Police Constable Tom Campbell; She (1965); Casino Royale (1967) as Carlton Towers, a British Foreign Office official, The Railway Children (1970) as Mr Albert Perks, the station porter and the Alfred Hitchcock thriller Frenzy (1972) as Felix Forsythe, the Covent Garden pub landlord.

[14] Cribbins was the narrator of the British animated children's television series The Wombles from 1973 to 1975 and also played the character of the Water Rat in a BBC Radio adaptation of The Wind in the Willows.

[19] In 1981, Music for Pleasure released a Swallows and Amazons audio book on tape cassette, read by Cribbins, abridged by Edward Phillips.

[26] These programmes concluded with Cribbins narrating a detective story as recurring character "Ivor Notion", with a script usually by Johnny Ball but sometimes by Myles Rudge, the co-writer of his Top 10 singles.

[28] He regularly appeared on BBC TV's The Good Old Days recreating songs made famous by the great stars of Music Hall.

[29][30] Among his later TV appearances were Dalziel and Pascoe (1999),[31] Last of the Summer Wine (2003),[2] Coronation Street (2003, as Wally Bannister)[31] and Down to Earth (2005).

The cast included Helen Lederer, Janine Duvitski and former Doctor Who companion Freema Agyeman in supporting roles.

On 9 May 2015, Cribbins gave a reading at VE Day 70: A Party to Remember in Horse Guards Parade, London which was broadcast live on BBC1.

In November 2018, it was announced that Cribbins would portray Private Godfrey in a series of re-creations of lost episodes from the BBC sitcom Dad's Army.

[8] He appeared in the BBC CBeebies Proms (Number 11 & 13) at the Royal Albert Hall on Saturday 26 & Sunday 27 July 2014 as Old Jack.

[36] National Life Stories conducted an interview (C1173/14) with Cribbins on his memories of Richard Negri in 2006 for its An Oral History of Theatre Design collection held by the British Library.

In 2022, Cribbins was reported to be returning to Doctor Who alongside David Tennant and Catherine Tate for the programme's 60th anniversary specials.