Dart studied keyboard instruments at the Royal College of Music in London from 1938 to 1939, and also studied mathematics at University College, Exeter, graduating in 1942. He became a music lecturer and later professor at the University of Cambridge. During his time at Cambridge, Dart did a lot of work for the early music revival. Musicians were becoming interested in playing music from the Baroque, Renaissance and even Middle Ages. He formed such groups as the Early Music Consort of London. In 1964 he became King Edward Professor of Music in the University of London (King's College).