A self-described late starter, Brabbins was born April 13, 1959. He attended Goldsmith's College and played in brass bands but had little other performing experience before studying conducting with Ilya Musin at the Leningrad Conservatory from 1986 to 1988. Upon his return to England, Brabbins won the 1988 Leeds Conductors Competition. His professional debut came that year as a last-minute substitute with the Scottish Chamber Orchestra. Within a few years, Brabbins had guest-conducted all the BBC orchestras and major and minor ensembles throughout England and Ireland. From 1994-2005, he was the associate conductor of the BBC Scottish Symphony Orchestra, and later added to his schedule the job of principal conductor of the contemporary music group Sinfonia 21. Brabbins expressed particular enthusiasm for "anything after Beethoven," especially such Russian composers as Tchaikovsky and Rachmaninov. He has also landed many opera engagements, mainly with England's lesser houses, conducting works ranging from Mozart standards to Bliss' The Olympians and Tchaikovsky's The Slippers. In 1997, he conducted the first commercial recording of Korngold's Die Kathrin.
Brabbins served as the artistic director of the Cheltenham Music Festival between 2005-2007. From 2009 to 2015, he was the principal guest conductor of DeFilharmonie (Royal Flanders Philharmonic) and was the chief conductor of the Nagoya Philharmonic in Japan from 2012 to 2016. Brabbins was named the music director of the English National Opera in 2016.
Brabbins has made more than 120 recordings for labels such as Chandos, NMC, and Deutsche Grammophon, along with Hyperion. His recorded efforts include a disc of Cyril Scott works with the BBC Philharmonic Orchestra (2004), Bax (2004), and Britten on Film (2009). He made numerous recordings with both the BBC Scottish Symphony Orchestra and the main BBC Philharmonic, often devoting his efforts to unfamiliar repertory from both Britain and continental Europe. His recording pace increased as the new century went on, and the year 2011 saw no fewer than eight Brabbins recordings. In 2020, he was heard on several releases, including a pair of Hyperion albums -- one offering music by Vaughan Williams, the other, music by James MacMillan -- and a BIS album containing works by John Pickard. Brabbins has taught as a visiting professor at the Royal College of Music.