Davis was born in Ebley, near Stroud, Gloucestershire the eldest of five children of Henry Frederick Alexander Davis, a solicitor, and his wife, Jessie Anna. The children were brought up by their mother, who moved to Weymouth in 1884 to open a school for young children including her own, and was successful enough to be appointed first headmistress of Weymouth College preparatory school in 1903. Davis attended Weymouth College from 1886 and went up to Balliol College, Oxford on a Brackenbury history scholarship, where he attained first classes in classical moderations in 1893 and "literae humaniores" in 1895 as well as the Jenkiyns exhibition. He was elected to a fellowship at All Souls College, Oxford, maintaining residence there from 1895 until 1902, and spending time teaching at University College, Bangor between 1896 and 1897. Davis won the Lothian Prize in 1897 and was appointed to a lectureship at New College, Oxford, and in 1899 exchanged lectureships and moved to Balliol, where on the expiration of his All Souls fellowship in November 1902 he was appointed a fellow of Balliol.