After college at Keele University, Finer travels around Europe and spends some time working on a barge in France. He settles in London and becomes the bass player in a group called The Petals and lives in 32 Burton Street, a house which he sometimes shares with Spider Stacey and Shane MacGowan. Together with James Fearnley they found The Pogues. Primarily a banjoist, he also plays other instruments, including mandola, saxophone, hurdy-gurdy, and the guitar. Apart from Shane MacGowan, Finer is the most prolific composer for the band.
Finer appears on all the band’s albums until their breakup in 1996. He continues working as a musician and composer after leaving The Pogues.
On January 1, 2000, the Finer-composed Longplayer piece of music is started and is designed to last 1,000 years without ever repeating itself. It currently exists in both computer-generated and live versions. Longplayer represents a convergence of many of his concerns, particularly those relating to systems, long-durational processes, and extremes of scale in both time and space.
Finer serves as “Artist in Residence” at the Astrophysics Sub-department of the University of Oxford between October 2003 and June 2005. Finer and Hamburg-based swamp pop legend DM Bob begin recording and performing together in 2005, releasing their album Bum Steer in August of that year and co-producing the debut album by experimental pop band Marseille Figs. In July 2005, Finer wins the PRS Foundation New Music Award on the basis of his proposal to build a device that will automatically “compose” a song of indeterminate length by harnessing the creative force of the weather.
In March 2012, Mobile Sinfonia, a global composition for ringtones is launched, developed during a year Finer spends as a non-resident artist at the University of Bath. This piece concerns mutual invasion of soundscape via ringtones.
Finer is currently working on a number of new projects continuing his interest in long-term sustainability and the reconfiguring of older technologies, including Spiegelei, a spherical camera obscura featuring Finer’s innovative 360-degree projection system and the Supercomputer in Cambridge, a 5-bit mechanical sculpture which will compute minimal musical scores.