She was born in London and studied piano at the Royal Academy of Music under Tobias Matthay. She became partiuclarly associated with contemporary British music, giving the world premiere of Ralph Vaughan Williams' Piano Concerto and recording Edward Elgar's Piano Quintet with the Stratton String Quartet under the composer's supervision. A number of composers wrote music specifically for her, particularly Arnold Bax (Cohen's lover) who wrote most of his piano pieces for her. This includes the music for David Lean's 1948 film version of Oliver Twist.
Cohen was made a CBE in 1938. She died in London.