He then became vicar of the Church of St. John the Evangelist, Carrington, leaving in 1994 following his appointment as vice-principal of St Stephen's House, Oxford, a position he took up in 1995.

In a column in the Catholic Herald, Burnham asked Pope Benedict XVI to provide a way for his parishioners to join him in the move.

[5][6] On 8 November 2010, Burnham was one of five Anglican bishops who announced their resignations and their intention to join the proposed personal ordinariate in England and Wales.

Also received at the same ceremony were Keith Newton (former Bishop of Richborough) and his wife, Gill, John Broadhurst (former Bishop of Fulham) and his wife, Judith, and three former sisters of the Society of Saint Margaret (Walsingham) — Carolyne Joseph, Jane Louise and Wendy Renate.

[9] On 13 January 2011, he was ordained to the diaconate with two other former Church of England bishops, John Broadhurst and Keith Newton.