Hopes was educated at Oxford High School until he moved to London in 1956, when he attended Enfield Grammar School. He then attended Warminster Theological College.
In 1963 he began a degree in theology at King's College London, taking his degree in 1966. He was ordained a Roman Catholic priest on 4 December 1995. For three years he served as assistant priest at Our Lady of Victories in Kensington, London, before becoming parish priest of the Holy Redeemer and St Thomas More Parish, Chelsea.
On 24 January 2003 he received episcopal consecration, along with the now Archbishop Bernard Longley, in Westminster Cathedral from Cardinal Cormac Murphy-O'Connor. The principal co-consecrating bishops were Bishop Arthur Roche of Leeds and Bishop Kieran Conry of Arundel and Brighton. In October 2010, Hopes was appointed as episcopal delegate of the Catholic Bishops' Conference of England and Wales for the implementation of the apostolic constitution Anglicanorum coetibus.
On 11 June 2013, Pope Francis appointed Hopes the fourth Bishop of East Anglia and installed on 16 July 2013 at St John the Baptist Cathedral, Norwich. In 2014, Hopes celebrated a historic Pontifical High Mass at the throne in his cathedral, for All Saints' Day. In June 2015, Bishop Hopes visited the Port of Felixstowe at the invitation of Apostleship of the Sea.
He went on board two ships and met with seafarers and blessed them. He also celebrated Mass at the port chapel.
In 2001, Hopes was appointed Vicar General of the Archdiocese of Westminster and in 2002 became a member of Bishops' Conference Committee for Liturgy and Worship. On 4 January 2003, at the age of 58, he was appointed an auxiliary bishop of Westminster, making him one of the most senior members of Catholic clergy to have converted in the 1990s.