Heffes was born in Beaconsfield, Buckinghamshire, and learned the piano from an early age. He graduated from Oxford University with first class honours and started his professional life playing keyboards and writing and arranging for commercials and TV (his band is featured playing in jazz club scenes in the film Circus). This led to him becoming assistant to composer Simon Boswell with whom he scored over 20 movies including A Midsummer Night's Dream and Cousin Bette. He also collaborated on Elton John's score to Women Talking Dirty and worked with members of Blur.[3][4]
In 2011 he released his first solo album, Face to Face. The album was created by improvising on location in a series of one on one collaborations with artists such as Regina Spektor, Ryuichi Sakamoto and Tunde Jegede. The tracks with Matthew Barley were recorded in the Turbine Hall of the Tate Modern in London.[3]