Edwyn Robert Bevan was the fourteenth of sixteen children of Robert Cooper Lee Bevan, a partner in Barclays Bank, and his second wife Emma Frances Shuttleworth, daughter of Philip Nicholas Shuttleworth, Bishop of Chichester. He was educated at Monkton Combe School and at New College, Oxford.
Bevan held an academic position at King's College London as Lecturer in Hellenistic History and Literature. The Arabist Anthony Ashley Bevan was his brother, the conspiracy theorist Nesta Helen Webster was his youngest sister and the artist Robert Polhill Bevan a cousin.
He married Mary Waldegrave, daughter of Granville Waldegrave, 3rd Baron Radstock in 1896 and they had two daughters, Christina (born March 1897, died 1981) and Anne (born March 1898,died 1983). A series of early colour photographs Mervyn O'Gorman took in 1913 of Christina dressed in red were included in the Drawn by Light exhibition in 2015 by the National Science and Media Museum and gained press and social media attention.