Ordained as a Roman Catholic priest in 1940, Wheeler was firstly an assistant curate at St Edmund's Parish in Lower Edmonton, then chaplain at Westminster Cathedral. He often made a point of noting to his clergy that he understood their difficulties from his having heard confessions every day of the 11 years he served in that office. He became chaplain to Catholics at the University of London in 1950. He was later named by the Holy See to the episcopate as the coadjutor bishop of the Roman Catholic Diocese of Middlesbrough in 1964, immediately after which he participated in the last two sessions of the Second Vatican Council. Wheeler was named Roman CatholicBishop of Leeds in 1966 and was an enthusiastic supporter of the spirit of the council. One example is that, immediately after his return from Rome, he founded a new ecumenical centre at Wood Hall in Wetherby, Yorkshire. Later, despite his feelings about the historic structure of the diocese, he followed part of its instruction by supervising the division of his diocese in 1980, in keeping with the conciliar mandate that dioceses be of such a size as to be truly manageable under the supervision of one bishop. Wheeler remained a staunch conservative in matters of liturgical practice. He was the last bishop in England to use the cappa magna and had a strong attachment to the Tridentine Mass. He submitted his resignation as bishop of the diocese at the mandatory age of 75 in 1985. He then entered an active retirement at the College of the Blessed Virgin Mary in Headingley under the care of the Little Sisters of the Poor.
Death and legacy
Wheeler died on 21 February 1998, aged 87, after a brief illness. At his request, he was buried near his predecessor and the bishop who had ordained him in the Catholic Church, Bishop Henry John Poskitt, also a convert from the Church of England, in the Church of St Edward the Confessor in Clifford, West Yorkshire. A noted author, Wheeler's memoir, In Truth and Love, was published in 1990. In March 2013, Catholic primary and secondary schools in north west Leeds and Bradford joined together to gain academy status from the government, as a Catholic multi-academy trust. The trust, the second in the Diocese of Leeds, took the name "The Bishop Wheeler Catholic Academy Trust". At present, 6 schools form the parts of the trust, however 10 other Catholic schools could join in the future.