Limb is best known for his work on Doctor Who, for which, between 1981 and 1985, he composed the music for the serials The Keeper of Traken, Four to Doomsday, Black Orchid,[3] Time-Flight, Arc of Infinity, Terminus, The Caves of Androzani and Revelation of the Daleks.
[4] Limb also contributed music to the television series The Justice Game, Aliens in the Family, The December Rose, Thinkabout, The Box of Delights, Kevin and Co, Martin Luther: Heretic, Storytime and the Look and Read serials "Fair Ground!
His music can also be found in documentaries, including Bellamy's Backyard Safari and Submarine: Perisher: Million Pound Captains.
He also composed and played "Swirley", a cheerful piece of electronic music that was used as the theme to the BBC's Service Information news bulletins in the late 1970s/early 1980s, and arranged the songs for several series of the BBC Schools programme You and Me, featuring Cosmo and Dibs.
[6] Limb was the composer of the music used in the Protect and Survive films, produced by the British government in the late 1970s to be broadcast in the event of imminent nuclear attack.