Finnegan first came to public attention with the Irish group Upstairs in a Tent, and then in 1993 he made a solo album When the Party's Over, which was recorded at Redesdale Studios. From 1995 he played with Flook, until they disbanded in late 2008. He is a frequent tutor for Folkworks and Burwell Bash. In 2009 he toured in California and Ireland with guitarist William Coulter. He also plays with an influential Russian rock group Aquarium, both live and on their studio albums (since approximately 2009).