Alfred Walter Saxon Snell was born in 1860, the second son of London-based hospital architect Henry Saxon Snell. Alfred was articled to his father 1877-80 and studied at University College and the Architectural Association. He was admitted ARIBA on 20 March 1882, his proposers being Lewis Henry Isaacs, Edward Cookworthy Robins and his father, who took him into partnership in the same year. He became FRIBA on 2 March 1891, his proposers being his father, Ernest Turner, and Alfred Williams. A third son, John Saxon Snell, born 1873, joined the practice as an apprentice in 1891 but left to commence independent practice in 1900. Henry Saxon Snell died in January 1904. His son Alfred continued the practice, taking Rees Phillips into partnership in 1921. The work of the firm was mainly connected with public baths, Poor Law infirmaries and similar buildings and hospitals.
He continued to take an active interest in the work of the firm until shortly before the Second World War. He married in 1884 and his wife died shortly after they had celebrated their diamond wedding. They had one son who was killed in action in the 1914-18 war and two daughters. He died on 8 June 1949