Byron was born and grew up in Cornwall, started playing trombone aged 9 and went on to study with Denis Wick. During 1988-1992 he studied at the Guildhall School of Music and Drama where he studied with Eric Crees.
In 1989 Byron performed the British premiere of Ranki's 'Tales of Father Goose' and since then has performed the Gordon Jacob and Launy Grondahl trombone concerti in London and the Ferdinand David 'Concertino' in Peru with the Lima Symphony Orchestra. In 2006 he performed the Derek Bourgeois Trombone Concerto with the RAF Central Band.
Byron has also performed at the International Trombone Festival in Helsinki, Finland (2003) and Birmingham, UK (2006).
Byron held the position of Co-Principal Trombone of the Orquesta Sinfónica de Galicia, Spain before returning to London to freelance in 1993. He then worked with a wide variety of orchestras and ensembles including the Chamber Orchestra of Europe, London Symphony Orchestra, Royal Philharmonic Orchestra and BBC Symphony Orchestra. Byron became Principal Trombone of the BBC Scottish Symphony Orchestra in 2000 and moved to the Philharmonia Orchestra in September 2001. In 2009 he became Principal Trombone of the London Sinfonietta.
Fulcher was featured as soloist in the 2004 Benjamin Zander / Philharmonia recording of Mahler's Third Symphony (although the CD sleeve calls him "Brian" Fulcher).
Byron has recently given masterclasses at the Trinity College of Music and Chetham's School of Music and can be heard on the soundtrack of the films Gladiator, Lord of the Rings and Curse of the Were-Rabbit. He also now teaches at the Royal College of Music and Birmingham Conservatoire and is a member of the London Brass.