Born in Hertfordshire, Peter Wright was educated at Highgate School and then spent two years as Organ Exhibitioner at the Royal College of Music, studying with Richard Popplewell (Organ) and Angus Morrison (Piano) and gaining various prizes and diplomas. In 1973 he went to Emmanuel College, Cambridge, as Organ Scholar where he continued his organ studies with Dame Gillian Weir and with Flor Peeters in Belgium. From there he was appointed Sub-Organist at Guildford Cathedral in 1977 and simultaneously held the post of Chief Conductor of the Guildford Chamber Choir, and of the Surrey Festival Choir.

In 1989 he was appointed Organist and Director of Music at Southwark Cathedral; a post he held for 30 years, and he remains an Honorary Lay Canon there. Following retirement Peter was appointed Interim Director of Music at Ripon Cathedral from November 2020 until December 2021 and, less than a year later, was Acting Director of Music at Jesus College, Cambridge to cover sabbatical leave.

Much in demand as an organ recitalist and choral conductor, both here and abroad, Peter enjoys a wide and varied repertoire. He has travelled widely in Europe, Japan and South Africa, and plays regularly with the country's leading orchestras, both solo and continuo. In 2018 he played a recital in Holy Trinity Cathedral in Auckland for the Congress of the New Zealand Association of Organists.

Peter Wright is a trustee of the Nicholas Danby Trust which seeks to support young organists of outstanding promise by awarding scholarships and bursaries for conservatoire study within Europe. In May 2011 he was awarded the prestigious FRSCM, in recognition of his work at Southwark and for church music in general, and he is also an Honorary Fellow of the Guild of Church Musicians. Now a Vice-President of the Royal College of Organists, Peter became a member of the Council in 1990 and was Chief Examiner from 1997 before becoming President (2005-2008).