In February 2017 the Boston Symphony Orchestra appointed Burton as Choral Director, a newly created position, and Conductor of the orchestra's Tanglewood Festival Chorus. He gave his Boston Symphony subscription series debut in 2018, and in April 2019 he replaced an indisposed Gustavo Dudamel to conduct a series of concerts with the Boston Symphony Orchestra and Tanglewood Festival Chorus at Boston Symphony Hall. Burton gave his Boston Pops Orchestra debut with Holiday Pops concerts at Symphony Hall in December 2017, and his Tanglewood Festival debut was in June 2019 with a Boston Pops concert of the music of Queen with Marc Martel. Burton founded the Boston Symphony Children’s Choir in 2018. Burton gave his debut with the National Symphony Orchestra of Mexico in 2016, and since then has been a frequent guest conductor. He led performances of Beethoven’s Symphony No. 9 in the Palacio de Bellas Artes to celebrate the orchestra’s 90th anniversary in 2018. In his native UK, Burton has conducted concerts with the Royal Liverpool Philharmonic Orchestra, the Orchestra of the Age of Enlightenment, the Hallé Orchestra, the Orchestra of Scottish Opera, Royal Northern Sinfonia, BBC Concert Orchestra and Manchester Camerata. He has conducted opera performances at English National Opera, English Touring Opera, and Garsington Opera where he won the Leonard Ingrams award in 2008. Burton's choral conducting has included the Gabrieli Consort, the Choir of the Enlightenment and the Wrocław Philharmonic Choir. In 2017 Burton conducted the BBC Singers at the inaugural season of Dubai’s Opera House as part of BBC Proms Dubai. From 2002 to 2009 he was Choral Director at the Hallé Orchestra and Conductor of the Hallé Choir, winning the Gramophone Choral Award in 2009 for a recording of Elgar's The Dream of Gerontius. Burton has worked frequently with young musicians, and is currently the conductor of the Boston Symphony Children’s Choir. He founded the Hallé Youth Choir in 2003, and from 2002-2017 he was the Music Director of Schola Cantorum of Oxford, leading the choir on international tours, recordings on the Hyperion label and appearing in BBC TV films about British composers made by John Bridcut.He founded the Schola Cantorum of Oxford conducting scholarship in 2011. In 2017 Burton was guest director of Japan’s National Youth Choir. Burton was Music Director of the St. Endellion Easter Festival from 2007 to 2013, succeeding Richard Hickox.
The Lost Words has 12 short movements which are settings of words from the award-winning 2017 book by Robert Macfarlane and Jackie Morris. Commissioned jointly by the Hallé Concerts Society and the Boston Symphony Orchestra, movements of the work were performed in 2019 by the Boston Symphony Orchestra and the Boston Symphony Children's Choir at the Tanglewood Festival, and by the Southbank Sinfonia and the National Youth Choir of Great Britainat the BBC Proms. The Convergence of the Twain SATB, Baritone Solo & Orchestra 18' The Convergence of the Twain was composed in commemoration of the 100th anniversary of the sinking of the Titanic in 2012, and is a setting of Thomas Hardy’s poem of the same name. The piece was premiered at the St Endellion Festival in 2012.