During Simple Minds' early to mid-1980s period, Burchill's guitar had a distinctive and atmospheric sound not dissimilar to Echo & the Bunnymen's Will Sergeant. Making heavy use of effects such as delay and chorus, his playing often provided subtle textures behind the band's more drum- and bass-propelled songs. This style was most apparent on 1982's New Gold Dream (81/82/83/84). From 1983's album Sparkle in the Rain onwards the group evolved a different style, bringing Burchill's playing more into the foreground.
As well as providing guitar, Burchill played the violin and saxophone on the band's first three studio albums and took over most studio keyboard duties following the 1989 departure of Mick MacNeil. Along with singer Jim Kerr, he is the only original member of the band left.