In 1980 he wrote two Christmas songs, "Christmas Bells" and "Imitation Myrrh", which he sang with Broom Leys Junior School choir, from Coalville, Leicestershire. The songs were sold as a record at Christmas throughout Leicestershire to raise money for the Leicestershire Arts and Music Association. These two, with other Christmas pieces of his composition, also appeared in The Truth about Christmas – or Gold, Frankenstein and Merv – a one-off television programme in 1984, performed by Stilgoe and children from the Broom Leys Junior School Choir.
Stilgoe is a fan of anagrams and in 1980 he wrote The Richard Stilgoe Letters; a Jumble of Anagrams, using characters made of anagrams of his own name. These included Chris Dogtailer and Giscard O'Hitler. He has appeared over 200 times on the daytime TV quiz show, Countdown, and hosted quiz shows such as The Year in Question on Radio 4, Finders Keepers (1981–1985), and Scoop (1981–1982). His 45-minute poem, "Who Pays the Piper?", outlined the history of music from Pan to the modern day, interspersing classical music with re-written lyrics. He also appeared on a satirical BBC TV show of the 1980s, A Kick Up the Eighties.