Stilgoe was born in Camberley, Surrey but brought up in Liverpool—where as lead singer of a group calling itself 'Tony Snow and the Blizzards' he performed at the Cavern Club. He was educated at Monkton Combe School in Somerset and at Clare College, Cambridge where he was a member of the Cambridge University Footlights.
In 1966 he played the role of Benjamin in the West End musical Jorrocks. He made his name on the BBC television teatime programme Nationwide, followed by Esther Rantzen's That's Life!, a light-hearted consumer affairs programme for which he wrote comic songs satirising various minor domestic misfortunes. His ability to write a song from almost any source material and at prodigious speed is part of his cabaret act, which includes such diverse gems as singing the instructions from a Swedish payphone; a pastiche of the King's Singers listing all the kings and queens of England in which he sings all four parts; and composing a song in the interval from a series of words and musical notes called out by the audience. He has also written and presented numerous BBC radio programmes, including Hamburger Weekend, Used Notes, Stilgoe's Around, Maestro and Richard Stilgoe's Traffic Jam Show, on BBC Radio 4.
Well known for his wordplay, Stilgoe is a great fan of anagrams and has appeared over two hundred times on the cult daytime TV quiz show Countdown. He once proudly announced on TV that an anagram of his name is Giscard O'Hitler. Stilgoe also hosted quiz shows, including The Year in Question on Radio 4, Finders Keepers (1981-1985), and Scoop (1981-1982). Stilgoe also wrote a famous 45-minute poem, Who Pays the Piper?, which humorously outlines the history of music from Pan to the modern day, interspersed with famous classical music with humorously re-written lyrics.
As well as being a comic of no small gift Stilgoe is a serious musician, writing lyrics for Starlight Express and collaborating with Charles Hart on the lyrics to The Phantom of the Opera and writing two musicals for schools, Bodywork and Brilliant the Dinosaur. Stilgoe gave away all his royalties for his work as lyricist on Starlight Express to a village in India. Such was the musical's success that for some years these donations were exceeding 500 Pounds a day. He has appeared on the Royal Variety Performance and presented the Schools Proms for over 20 years, and has toured extensively both solo and with Peter Skellern.
In 1980 he wrote two Christmas themed songs, Christmas Bells and Imitation Myrrh which he sang with Broom Leys Junior School Choir, from Coalville in North West Leicestershire, England. The songs were released as a single vinyl record at Christmas throughout the county of Leicestershire to raise money for Leicestershire Arts and Music Association (LAMA) and reached number 1 throughout the county of Leicestershire.
He founded the Orpheus Trust in 1998, based in a previous family home in Godstone, Surrey, offering performing arts experiences to young people with various disabilities; he also started the Stilgoe Family Concerts series at the Royal Festival Hall, which feature young performers and regular commissions of new music.
He was High Sheriff of Surrey in 1998–99, and has a great interest in the sport of cricket, being appointed President of Surrey County Cricket Club in 2005. He has also been President of the Lord's Taverners.
Stilgoe has two Tony nominations, three Monte Carlo Prizes, a Prix Italia, an honorary doctorate and an OBE to his name. He is well-known for his love of architecture (both building it and demolishing it), having designed and built his own house more than once, and owns his own mechanical digger.