As a boy Parnell was a choral scholar at Southwell Minster, where he began organ studies under Kenneth Beard. He won the Organ Scholarship at Christ's College, Cambridge aged 19 and studied under Nicolas Kynaston. He was awarded the Fellowship Diploma of the Royal College of Organists aged 19 and won the Limpus and Shinn prizes in that year's FRCO diploma examinations.
After a spell as Director of Music at St James's Church, Cambridge, he moved to St Albans in 1976 as Assistant Master of the Music to the Cathedral and Abbey Church of St Alban, appointed by Peter Hurford. He was also appointed Master of Music and choirmaster at St Albans School. He founded St Albans Abbey Girls' Choir in 1996, which is now a regular part of the worshipping community. From 1983 to 2001 he conducted St Albans Symphony Orchestra. In 2001, after 25 years in St Albans, he moved to Norfolk for a few years, but has subsequently returned to live in St Albans where he is pursuing his freelance organist and recording career.
He is a trustee of the New School of Organ Studies 
Recording and performing career
Parnell has accompanied St Albans Cathedral Choir in recordings and radio and television broadcasts and has also accompanied Norwich Cathedral Girls' Choir on tour in the Netherlands, deputised as Assistant Organist at Southwell Minster and at the Cathedrals of Ely, Canterbury and Wakefield, and is conductor of Ely Choral Society, principal conductor of Cambridgeshire Choral Society and Wymondham Symphony Orchestra. He has also made numerous solo recordings on the organ and harpsichord.