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Innes graduated with a Bachelor of Arts in Fine Art from Goldsmiths' in 1966.[2][3] During the period of 1962 to 1965, Innes and several other art school students started a band which was originally named The Bonzo Dog Dada Band after their interest in the art movement Dada, but which was soon renamed the Bonzo Dog Doo-Dah Band (later shortened to The Bonzo Dog Band). Innes, with Vivian Stanshall, wrote most of the band's songs, including "I'm the Urban Spaceman", their sole hit, (produced by Paul McCartney) and "Death Cab for Cutie" (which inspired an American musical group of the same name), which was featured in The Beatles' film Magical Mystery Tour. Innes won an Ivor Novello Award for Best Novel(ty) Song in 1968 for "I'm the Urban Spaceman"
In the late 1960s, Innes appeared with the Bonzo Dog Band on both seasons of the UK children's television series Do Not Adjust Your Set which also featured some future members of the Monty Python comedy team.
After the break-up of the Bonzo Dog Band, Innes joined with former Dog Band bassist Dennis Cowan, drummer Ian Wallace and guitarist Roger McKew to form The World, a band hoping for "more commercial" success with music ranging from rock to pure pop, yet still retaining some Doo-Dah flavour and even some of the humour.
In the mid-1970s, Innes became closely associated with the TV series Monty Python's Flying Circus. He played a major role in performing and writing songs and sketches for the final series in 1974. He wrote a squib of a song called "George III" which appears in "The Golden Age of Ballooning". He also wrote the song "Where Does a Dream Begin?", used in "Anything Goes: The Light Entertainment War". He co-wrote the "Most Awful Family in Britain" sketch and played a humorous stilted guitar version of the theme song, The Liberty Bell March, during the credits of the last episode, "Party Political Broadcast". He is one of only two non-Pythons to ever be credited writers for the TV series.
He appeared on stage with the Pythons in New York City in 1976, performing the Bob Dylanesque "Protest Song" (complete with harmonica) on the album Monty Python Live at City Center. He was introduced as Raymond Scum. After his introduction he told the audience "I've suffered for my music. Now it's your turn." In 1982 he travelled to the States with the Pythons again, appearing in Monty Python Live at the Hollywood Bowl. He performed the songs "How Sweet to Be an Idiot" and "I'm the Urban Spaceman". He also appeared as one of the singing "Bruces" in the Philosopher Sketch.
Innes wrote the songs for Monty Python and the Holy Grail. He appeared in the film as a head-bashing monk, the serf crushed by the giant wooden rabbit, and the leader of Sir Robin's minstrels. He also had a small role in Terry Gilliam's Jabberwocky. Because of these long-standing connections, Innes is often referred to as "the Seventh Python".
After Python finished its original run on UK television, Innes joined with Python's Eric Idle on the series Rutland Weekend Television. This was a Python-esque sketch show based in a fictional low-budget regional television station. It ran for two series in 1975–76. Songs and sketches from the series appeared on a 1976 BBC LP, The Rutland Weekend Songbook. This show spawned The Rutles (the "prefab four"), an affectionate pastiche of The Beatles, in which Innes played the character of Ron Nasty, who was loosely based on John Lennon. Innes played Nasty in an American-made spin-off TV movie, All You Need Is Cash, with Idle. The project also yielded the commercially successful soundtrack album The Rutles released by Warner Brothers.

