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".