Varah was initially reluctant to follow his father's vocation, but his godfather persuaded him to study at Lincoln Theological College, where he was taught by the Revd Michael Ramsey, later Archbishop of Canterbury. He was ordained deacon in the Church of England in 1935 and priest in 1936. He first served as curate at St Giles, Lincoln, from 1935 to 1938, then at St Mary's, Putney, from 1938 to 1940 and Barrow-in-Furness from 1940 to 1942. He became vicar of Holy Trinity, Blackburn, in 1942 and moved to St Paul, Battersea, in 1949. He was also chaplain of St John's Hospital, Battersea.