He debuted on stage at the West End in 1956 in A Comedy of Errors and continued in theatre shows for the rest of the '50s, and then released three comedy songs in 1962. They were produced by The Beatles producer George Martin and were very successful in the UK Singles chart, his last one being "Gossip Calypso" which just about scraped the top 30. The band Right Said Fred (of "I'm Too Sexy" fame) are named after one of his other songs.
Cribbins' first film appearance was Two Way Stretch in 1960 and mostly stuck with comedies. In 1963 and '64, he briefly joined the popular Carry On film series as the leading straight man in Carry On Jack and Carry On Spying, which were really successful at the British box office. Two years later, he appeared in the Doctor Who movie Daleks' Invasion Earth: 2150 A.D. as Constable Tom Campbell and featured in She, and appeared in '70s films Frenzy and The Railway Children.
At this point, Cribbins mostly appeared in voice acting, particularly for children's TV shows. He did the voices for the characters from The Wombles and appeared over 90 times in Jackanory, and voiced cartoon mascots for TV business commercials, as well as a couple of radio appearances.
Cribbins has made some appearances on television as well. He returned to the Doctor Who scene in the mid-2000s to portray the grandfather of the Tenth Doctor's companion and gave a memorable appearance on the 2009 Christmas special on the departure of David Tennant from the series. He's also featured in The Avengers, Worzel Gummidge and even had a TV series of his own called Cribbins on ITV.
In the 2010s, Cribbins continues to make brief appearances on television, but mostly sticks to appearing onstage around the UK; young children that watch CBeebies may have watched his show Old Jack's Boat. He received an OBE in 2011 for his services to drama and received the JM Barrie award in 2014.