After finishing his studies at Clare College, Cambridge, Cohen began his professional career by establishing himself as a cellist.

He was a founder member of the London Haydn Quartet in 2000 and continues to perform chamber music with friends and colleagues.

Cohen is Artistic Director and founder of the British early music ensemble Arcangelo, which he founded in 2010[1] as an outgrowth of his assembling an orchestra for a recording project with Iestyn Davies, whom he had known since university.

[3] Cohen is Artistic Partner of the Saint Paul Chamber Orchestra (Minnesota, US) and Associate Conductor of Les Arts Florissants.

[2] On 6 October 2016, the Quebec City-based period orchestra Les Violons du Roy named Cohen its next music director, effective with the 2017–2018 season.