Born in Belfast, Burke's first band was St. Vitus Dance, which released the album Love Me, Love My Dogma in 1987 before splitting up a few years later. Shortly after the split, Burke was contacted by Will Sergeant and eventually joined the Bunnymen as lead vocalist. The band released Reverberation (1990) to mixed reviews, though the album has subsequently garnered some acclaim. The Bunnymen formally announced their disbandment in 1993, after which Burke became a teacher.
In 2005, Burke reformed St. Vitus Dance for some live shows, and an album of new material, Glyphotheque, was released in 2008.