The Bishop of Durham is the Rt Revd Paul Butler. You can contact him by email or via his PA Jo Dowset on 01388 311944.
The Bishop of Durham is the diocesan or most senior bishop, responsible for oversight of the whole diocese.
The Bishop of Durham  is the Anglican bishop responsible for the Diocese of Durham in the Province of York. The diocese is one of the oldest in England and its bishop is a permanent member of the House of Lords. Paul Butler has been the Bishop of Durham since his election was confirmed at York Minster on 20 January 2014. The bishop is one of two (the other is the Bishop of Bath and Wells) who escort the sovereign at the coronation.
He is officially styled The Right Reverend Father in God, (Christian Name), by Divine Providence Lord Bishop of Durham, but this full title is rarely used. In signatures, the bishop’s family name is replaced by Dunelm, from the Latin name for Durham (the Latinised form of Old English Dunholm). In the past, Bishops of Durham varied their signatures between Dunelm and the French Duresm. Prior to 1836, the Bishop of Durham was a prince-bishop and had significant temporal powers over the Liberty of Durham and later the County Palatine of Durham.
The bishop lived in Durham Castle from its construction in the 11th century. In 1832, Auckland Castle became the official residence of the Bishops of Durham until July 2012 when ownership of the castle was transferred over to the Auckland Castle Trust, a charitable foundation with the aim of beginning a major restoration of the grounds and castle and creating permanent exhibitions on the history of Christianity in Britain and the North East. The bishop continues to have offices in Auckland Castle but no longer resides there.
 – Wikipedia entry https://en.wikipedia.org/wiki/Bishop_of_Durham [February 2018]