Cribbins made his first West End theatre appearance in 1956 at the Arts Theatre playing the two Dromios in A Comedy of Errors and went on to co-star in the first West End productions of Not Now Darling, There Goes the Bride and Run For Your Wife. He also starred in the revue An Another Thing, and recorded a single of a song from the show entitled "Folksong". In 1962 he recorded two highly popular and well-remembered comedy records, "Right Said Fred" (in which a group of workmen struggle to relocate a large unspecified object, possibly a piano) and "Hole in the Ground" (in which an embittered workman murders a bowler-hatted harasser).
Cribbins appeared in films from the early 1950s, his portfolio including three Carry On films, the second Doctor Who film Daleks - Invasion Earth 2150 AD, and as the station porter, Perks, in The Railway Children. He was the narrator of the British animated children's TV series The Wombles. He also narrated a celebrated BBC radio adaptation of The Wind in the Willows and provided the voice of the Tufty character in RoSPA road safety films in the 1960s. He holds the record for reading the most episodes of Jackanory, with a total of 111 appearances. Other television appearances included Fawlty Towers, as the spoon salesman Mr. Hutchinson (mistaken by Basil Fawlty for a hotel inspector) in the episode "The Hotel Inspectors" (1975). He also provided the voice of Buzby, a talking cartoon bird that served as the mascot for the then General Post Office, He also appeared reduced to OO gauge in adverts for Hornby model trains.
In 2003 he played Wally Bannister in the long running soap Coronation Street. He is also the narrator of The Way We Were, a 2008 series broadcast on ITV.
In 2007 he appeared as Wilfred Mott in the Doctor Who Christmas special, "Voyage of the Damned"; he then reappeared as the same character throughout the 2008 series, as the grandfather of companion Donna Noble. Writer Russell T Davies confirmed on BBC Breakfast that Cribbins would return to the programme as the Doctor's companion in the last two specials to be screened at the end of 2009.