Davis was born in the U.K. in 1972. He attended the Royal Academy of Music, studying composition with Justin Connolly and graduating in 1994.
Among Davis' extensive television credits is one for a sequence in the "Diggs" episode of season 25 of The Simpsons, a riff on the series' venerable couch gag that has been viewed on YouTube more than six million times. He has written 12 television series soundtracks, music for 15 short films, two major British films for television, and soundtracks for feature films in Britain (The Ringer) and the U.S. (An Unkindness of Ravens and Sleepwalk with Me). Davis has also written songs, including one called Song for Malala, both for and independently of dramatic productions. His ballet scores, executed as part of collaborations with choreographer Erico Montes, include the well-reviewed Within the Hours.
Davis began to gain widespread exposure in 2015 with the release of the album Flight, featuring his music as recorded by violinist Kerenza Peacock and the London Symphony Orchestra. The release was named Featured Album of the Week on Britain's popular Classic FM radio network, gained wide radio airplay in many countries, and cracked top levels on both British and U.S. classical sales charts. A selection of pieces from the album, which does not fit easily into the categories of crossover, minimalist, or neo-Romantic, was made into the ballet Flight of Fancy and performed in 2016 by the Tulsa Ballet in the state of Oklahoma. The album spawned the equally successful Seasons, which includes songs based on the sonnets depicted by Vivaldi's Four Seasons violin concertos. A third album in the series, Liberty, appeared in early 2018.