He taught Classics, Philosophy and Theology at Ushaw from 1918 to 1930, the year when he was appointed rector of the English College, Rome and given the title Monsignor (28 October).

In 1935, Godfrey was made a member of the Pontifical Commission to Malta, and attended in an official capacity the 1937 coronation of King George VI and Queen Elizabeth.

On 21 November 1938, Mgr Godfrey was appointed Titular Archbishop of Cius and first Apostolic Delegate to Great Britain, Gibraltar and Malta.

Godfrey, who was the first papal representative to England since the Reformation,[4] received his episcopal consecration on the following 21 December, in the chapel of the English College from Cardinal Raffaele Rossi, OCD, with Archbishop Luigi Traglia and Bishop Ralph Hayes serving as co-consecrators.

Pope Pius XII appointed Godfrey Archbishop of Westminster, and thus the ranking prelate of the Catholic Church in England and Wales, on 3 December 1956.