Ffoulkes was educated at Shrewsbury School and Jesus College, Oxford. His uncle, Henry Foulkes was principal of the college from 1817 to 1857. He obtained a second-class degree in Literae Humaniores in 1841. He became a Fellow of Jesus College in 1843, holding this position until 1855. He was ordained as a priest in the Church of England and also served for a time as the college's Junior Bursar. He joined the Roman Catholic Church in 1855. However, after fifteen years in the Catholic Church, he applied to his Bishop, Samuel Wilberforce, to be reinstated as a clergyman in the Church of England, and his request was granted. Jesus College appointed him as rector of Wigginton, Oxfordshire in 1876. When the position of vicar of the University Church of St Mary the Virgin in Oxford became vacant in 1878, no Fellow of Oriel College wished to accept the appointment and the position was then offered to Ffoulkes, who had previously assisted at services.
Ffoulkes wrote several theological works, including Christendom's Divisions, The Church's Creed or the Crown's Creed, and The Primitive Consecration of the Eucharistic Oblation. His final work was The History of St. Mary the Virgin. He also lectured in Divinity to the non-collegiate students at Oxford.
- "Rev. Edmund Salisbury Foulkes". The Times. 21 April 1894. p. 12.
- Baker, J. N. L. (1954). The Victoria History of the County of Oxford Volume III – The University of Oxford. The University of London Institute of Historical Research. p. 278.
- Hardy, Ernest George (1899). "Appendix III – List of Fellows". Jesus College. London: F. E. Robinson & Co.