He attended Canford School in Wimborne in Dorset. Originally a chorister at King's College, Cambridge, he approached Boris Ord for organ lessons, but was referred to Hugh McLean. Preston then studied the organ with C. H. Trevor before returning to King's as organ scholar.
He was sub-organist of Westminster Abbey from 1962 to 1967, and organist of Christ Church, Oxford from 1970 before returning to Westminster as Organist and Master of the Choristers in 1981. He relinquished his Westminster post in 1987, and has since led an international concert career, and has also composed works for the organ, the best-known of which is probably his Alleluyas, written in the style of Olivier Messiaen.
In 1965, for the Edington Music Festival, he commissioned Psalm 119 verses 73-104 and in 1966 a set of 5 proper anthems. In 1967, Preston wrote a setting of a Missa Brevis (Short Communion Mass) for Edington Music Festival. Also in 1968, he wrote a Magnificat and a Nunc Dimittis for the same festival.
His recordings include the complete organ works of J. S. Bach and the Saint-Saëns Organ Symphony, with James Levine conducting the Berlin Philharmonic Orchestra, both for Deutsche Grammophon. He has played harpsichord (particularly earlier in his career), including on a recording of the Concert Champêtre, as well as organ. He has recorded Handel's complete organ concertos twice: with Yehudi Menuhin conducting the Bath Festival Orchestra and then later on period instruments with Trevor Pinnock directing The English Concert. In 2010, he played the organ for the recording of Berlioz's Te Deum op.22, with The BBC National Orchestra of Walles, conducted by Susanna Mälkki (CD BBC Music Magazine 2010). Already an Officer of the Order of the British Empire (OBE), Preston was promoted Commander of the Order of the British Empire (CBE) in the 2009 Birthday Honours.