In 1871 Edmundson was elected to an Open Fellowship at Brasenose and was Mathematical Lecturer there from 1871 to 1880 and also a college tutor from 1875 to 1880. He was ordained a deacon of the Church of England in 1872 and a priest in 1874. From 1875 to 1881 he was Junior Bursar of his college and in the University was Mathematical Examiner for Final Honour Schools for 1875–76. In 1880, Edmundson accepted the benefice of Northolt, Middlesex, where he remained until 1906, when he became Vicar of St Saviour's, Upper Chelsea, retiring in 1920. He was also Rural Dean of Chelsea from 1916 to 1920. From 1896 to 1899, Edmundson worked for the British Government in the matter of a Boundary Arbitration between British Guiana and Venezuela, and from 1901 to 1904 he worked for the government again on a Boundary Arbitration between British Guiana and Brazil. His work was research, under the direction of Sir Charles Alexander Harris, who later wrote "To the staff who worked under my direction in the two Guiana arbitration cases, where extreme accuracy and patience were required, I find it difficult to record my indebtedness. Mr de Villiers, my co-editor of Storm, and Dr Edmundson were with me throughout." One of Edmundson's major works, The Church of Rome in the First Century, appeared in 1913, having originated as the Bampton Lectures for that year. Much later, J. A. T. Robinson praised it highly. In his Redating the New Testament, he noted that Edmundson's book had largely been ignored at the time, perhaps because he was not a professional New Testament scholar and his conclusions were radically different from the consensus of the "higher criticism" of his day. In 1917–18, Edmundson worked for the Foreign Office's Historical Department. He married Florence Brooke Turner, the daughter of Joseph Brooke Turner, of Edgerton, Yorkshire, and they had one son and one daughter. He retired to a house named the Villa Nicette, at Saint-Raphaël in the south of France and died on 3 July 1930.
Honours
Foreign Member of the Netherlands Association of Literature, 1886
Milton and Vondel, a Curiosity of Literature, 1885
The Swedish Legend in British Guiana: an historical investigation
'The Revolt of the Netherlands', 'William the Silent' and 'The Dutch Republic' in Cambridge Modern History, vol. III The Wars of Religion
Archbishop Laud and his Work, 1905
'The Administrations of John de Witt and William of Orange ' in Cambridge Modern History, vol. V The Age of Louis XIV
Anglo-Dutch Rivalry in the First Half of the 17th Century, 1910
Intellect and Power, the Pride Sermon, 1912
The Church in Rome in the First Century: an examination of various controverted questions relating to its history, chronology, literature and traditions: eight lectures preached before the University of Oxford