Babbington started his musical career in 1958, playing double bass in local jazz bands. At the age of 17 he took up the post of double bass, doubling on electric guitar with The Leslie Thorp Orchestra at the Aberdeen Beach Ballroom, where he honed his sight reading skills. After moving to London in 1969, he joined the bandDelivery, one of the side roots of the Canterbury scene with Phil Miller, Pip Pyle and Lol Coxhill. Also, he began to work as a session musician with jazz/fusion musicians like Michael Gibbs and The Keith Tippett Group, appearing on their album Dedicated To You But You Weren't Listening as well as in Tippett's big band project Centipede and on Dean's album Just Us. When Delivery disbanded in 1971 after an album with Carol Grimes titled Fools Meeting, Babbington joined Nucleus. He contributed to albums by Alexis Korner, Mike d'Abo, Chris Spedding, folk singers Harvey Andrews and Schunge, and was a part-time member of the bands Solid Gold Cadillac and Keith Tippett's Ovary Lodge.
With Soft Machine
Having already contributed additional double bass parts to electric bassist Hugh Hopper's work on the Soft Machine albums Fourth and Fifth, he finally replaced Hopper fully in the band with the release of their album Seven. He used a six-string Fender VI throughout his tenure with the band. In addition to Seven, he can be heard on BBC Radio 1971-1974, Bundles, Softs and the library music project Rubber Riff. Babbington's funk- and rock-oriented electric bass playing went along well with Karl Jenkins' and John Marshall's fusion concept of Soft Machine at the time.
After 1976
After leaving Soft Machine, Babbington remained active on the UK jazz scene, playing with Barbara Thompson's Paraphernalia, Joe Gallivan's Intercontinental Express and various bands led by pianist Stan Tracey. In 1979, he appeared on the albumWelcome to the Cruise by Judie Tzuke. In the 1980s and 90s, he returned to his roots, double bass and pure jazz, and became affectionately known by the musical community as the jazz handbrake. He also worked with Elvis Costello, Carol Grimes, Mose Allison and the BBC Big Band. In 2008, he played with Soft Machine Legacy and has replaced Hugh Hopper as their electric bassist in 2009. Soft Machine Legacy changed their name back to just Soft Machine in 2015.
Personal life
Babbington has a daughter by the name of Nicola Babbington & sons Gary Mery and Nick Babbington.