Educated at Blundell's School, he later studied both music and law at Jesus College, Cambridge, graduating with dual degrees, subsequently obtaining a reputation for both musical scholarship and organ playing. Hurford subsequently studied in Paris under the blind French organist André Marchal, exploring music of the Baroque period.
He is best known for his interpretations of Bach, having recorded the complete Bach organ works for Decca and BBC Radio 3. His expertise also encompasses recordings of the Romantic literature for organ, performances notable for attention to stylistic detail. His playing style is noted for clean articulation, beauty of expression, and a sense of proper tempi.
He is the holder of a number of Honorary Doctorates, was appointed an Honorary Fellow of Jesus College in 2006, received the Medal of the Royal College of Organists in 2013, and has been appointed an Officer of the Order of the British Empire OBE. He has written a book: Making Music on the Organ (1998, Oxford University Press, ISBN 0-19-816207-3) and published a deal of choral music for the Anglican liturgy, much of it issued by leading publishers such as Novello and Oxford University Press. His Litany to the Holy Spirit, to a famous text by Robert Herrick, is sung worldwide.