Neylon carried out his studies in preparation for the priesthood at Saint Joseph’s College in Upholland and then at Saint Cuthbert’s College in Ushaw.
On 31 May 1982 he was ordained a priest at Heaton Park Manchester by Pope John Paul II, during his historic papal visit to Britain, for the Archdiocese of Liverpool.
He subsequently served as parish priest at Saint Cuthbert’s, Wigan (1982-1986) and then in Skelmersdale (1986-1996).
In 2006 he became Dean of the pastoral zone of Saint Helens, and in 2007 vicar general.
On 6 July 2021, Pope Francis appointed him Auxiliary Bishop of Liverpool, with the Titular See of Plestia.