Cohen was born in Manchester on November 17, 1977. He attended the Royal Northern College of Music, studying with cellist Emma Ferrand, and then moved on to Clare College, Cambridge, where he studied music and graduated in 2000. During the first part of his career, Cohen was active mostly as a cellist, performing with both mainstream and historically oriented ensembles, including the Philharmonia Orchestra, the Scottish Chamber Orchestra, and the Orchestra of the Age of Enlightenment. Becoming more interested in conducting and chamber music performance, he founded the Picander Ensemble in 2004. In the late 2000s decade, Cohen collaborated with violinist Benjamin Nabarro, violist Lawrence Power, and pianist Daniel Tong in performances of piano quartet repertory at London's Wigmore Hall and many other major venues and festivals. He served as an assistant conductor to William Christie with the early music group Les Arts Florissants and Emmanuelle Haïm with Le Concert d'Astrée, and in 2010, he founded the early music group Arcangelo. This ensemble has been internationally successful, making several appearances at the BBC Proms and performing at the Philharmonie in Berlin, the Musikverein in Vienna, and Carnegie Hall in New York, among other venues. Cohen has also served as an artistic partner with the Saint Paul Chamber Orchestra and as the artistic director of Britain's Tetbury Festival. In 2018, he was named the music director of Les Violons du Roy. Cohen is an enthusiastic conductor of Classical-period repertory as well as the usual Baroque material featured by early music groups.
Cohen's more than 20 recordings display his full range of talents. With Arcangelo, he has recorded mostly for the Hyperion label, though he has also released albums on Archiv, Berlin Classics, Signum Classics, and other labels. In 2021, Cohen and Arcangelo moved to the Alpha label for a new recording of Handel's Brockes-Passion, HWV 48, featuring soprano Sandrine Piau. ~ James Manheim, Rovi