Burgess was born in Britain. His father had eclectic musical tastes that included rock, experimental music, classical music, opera, and music of the world. Burgess started taking piano lessons at seven. He was unenthusiastic about those, but his musical interests were awakened, and he started buying records and writing his own songs, using a piano and committing them to a four-track tape recorder. As a youth, Burgess dreamed of singing in a pop band, but in secondary school, he spotted the school's drum kit and took to it immediately, convincing teachers to let him teach himself because there were no lessons available. He made rapid progress, and at 12, he was playing in jazz groups with musicians from 16 to 18 years old. At 16, he began studying percussion with Jayne Obradovic; at that time, he was first exposed to the marimba, which became one of his main instruments. Burgess attended the Guildhall School of Music and Drama in London, studying classical percussion and becoming acquainted with electronics. He "worked my arse off for five years, developed my listening, and got more and more into playing music at the experimental end of the scale," he told Tobias Miorin.
After graduating, Burgess joined the Bash Ensemble, an experimental percussion group, replacing his teacher Richard Benjafield in 2001. He remained with the group for 16 years, playing some 50 concerts a year even as he became better known on his own. In 2005, Burgess formed Powerplant, collaborating with sound designer Matthew Fairclough and visual artist Kathy Hinde. The music of the group combined percussion, electronics, and original visual art on a backdrop screen. Burgess has also performed as a soloist around Britain, Europe, and the U.S. He has toured with Peter Gabriel, Stewart Copeland, and other rock artists, and his work has been heard on soundtracks to films such as Black Panther, The Darkest Hour, and Paddington 2. Burgess has recorded for the Signum label with Powerplant (the 2012 album 24 Lies Per Second), with orchestra (Gabriel Prokofiev's Bass Drum Concerto, with the Ural Philharmonic in 2019), and solo (an album of his own marimba arrangements of choral music by Eric Whitacre in 2020). He has taught percussion at the Junior Trinity youth music program. ~ James Manheim, Rovi