[2] He was strongly influenced by the Anglo-Catholic tradition of the church in Worsley which he attended during his time at the grammar school.
[4] From 1932 to 1933, Wheeler trained for holy orders in the Church of England at St Stephen's House, Oxford.
[2] He was firstly an assistant priest at St Edmund's Parish in Lower Edmonton from 1940 to 1944, then chaplain at Westminster Cathedral.
[2] 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 at the cathedral.
[2] Wheeler was 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 Catholic Bishop of Leeds in 1966 and was an enthusiastic supporter of the spirit of the council.
He then entered an active retirement[4] at the College of the Blessed Virgin Mary in Headingley under the care of the Little Sisters of the Poor.