Auxiliary Bishop Swindlehurst died on 28 August 1995 and was not replaced, leaving Bishop Griffiths to administer the diocese without the assistance of any auxiliary. He implemented a number of changes to the structure of the diocese in order to ease transition to a new model of administration, and these measures included appointing new vicars general to assist the bishop. Throughout his tenure, Bishop Griffiths worked closely with young people, establishing a Youth Mission Team in the diocese and representing young Catholics in the Catholic Bishops' Conference of England and Wales.
He served as leader of the Diocese of Hexham and Newcastle for twelve years. When he reached the age limit for bishops of 75 years, prescribed in the Code of Canon Law for the Latin Rite branch of the Catholic Church, he submitted his resignation to John Paul II. His resignation was accepted and he retired on 25 May 2004, the memorial of Saint Bede, the Venerable. On the same day, he presided at the consecration of Kevin Dunn, who succeeded him. After retiring, he moved to St Mary's parish in Leyland, Preston, Lancashire and continued in his work as a member of the Catholic Bishops' Conference of England and Wales. [citation needed]
Following a serious illness, due to acute leukaemia, he died, aged, 82, at Saint Mary's, during the afternoon of 14 June 2011. He is buried at Ampleforth Abbey.