Brough was born in London on July 15, 1963. He attended the Royal College of Music in London, studying piano, singing, and percussion. His involvement with English choral singing began when he held organ scholarships at St. Michael's College, Tenbury, and Magdalen College, Oxford. He went on for conducting courses at the Royal Academy of Music, also beginning his educational career as a lecturer in the Department of Music at King's College, London, during this period. In 2004, he became a professor of music at the Royal Academy, and he has trained a group of conducting students privately. Brough's career as a conductor developed with a stint as assistant to Sir Jeffrey Tate during a production of Wagner's Ring Cycle in 2007-2009. He served as guest chorus master at the English National Opera, as acting organist of New College, Oxford, and as Acting Precentor of Gonville and Caius College, Cambridge. Brough was the principal conductor of the historically oriented orchestra The Hanover Band from 2007 to 2010. He conducted church choirs at All Saints Margaret Street in London, Sheffield Cathedral, and Tewkesbury Abbey, and in 2011, he made his recording debut, leading the Choir of All Saints Margaret Street in an album of music by Harry Bramma on the Priory Records label.
From 2011 to 2016, Brough was the principal guest conductor of the BBC Singers. He made several recordings with that group, including My Dancing Day: Choral Music by Richard Rodney Bennett (2012) and I Am the Song: Choral Music by Bernard Hughes (2016), both on the Signum Classics label. With the BBC Singers, he conducted 60 broadcast concerts of choral music from around the world. In 2015, Brough became Director of Music at St. Mary's, Bourne Street, in London's posh Belgravia neighborhood. He has guest conducted many of Britain's leading orchestras, including the BBC Symphony, the Royal Philharmonic, and the BBC Concert Orchestra. Brough was named Director of Music at Keble College, Oxford, in 2020, and as the college's choir emerged from the coronavirus pandemic, he led it in his debut recording with the group, Resurrexi!: Easter in Vienna with Mozart and the Haydn Brothers, released on the CRD label in 2022. ~ James Manheim, Rovi