Buxton has been at the forefront of British comedy since at least the 1990s. His skills as a writer, director and actor have not only seen him in steady work since his early twenties, but have also transformed him into a personality equally likely to appear on British television as himself or as a character. In 2011, he hosted the long-running musical quiz show Never Mind the Buzzcocks with Phill Jupitus.
He first came to light in a comedy duo with longtime friend Joe Cornish, with whom he wrote and starred in The Adam and Joe Show. He was a writer on Big Train, a Simon Pegg sketch comedy show that was also one of Catherine Tate's first gigs.
As an actor, he guest-starred in some of the biggest British comedies of the 2000s, including Randall & Hopkirk (Deceased) with Tom Baker and Matt Lucas; Look Around You with Olivia Colman and Andrew Burt; The IT Crowd with Katherine Parkinson; and Hot Fuzz with Simon Pegg.