William Henry Bevan was born in Bristol, Gloucestershire, England in 1865 and was articled to John Bevan (c.1843-1945) in Bristol in 1882. He also attended classes at University College, Bristol. From 1888 he worked as an an architectural assistant for Hull Corporation. In 1892 he commenced independent practice in Cardiff, Wales, and between 1896 and 1902 he was employed in the War Office, barrack design branch. He qualified as an architect in 1902 and later that year was elected an Associate of the Royal Institute of British Architects (A.R.I.B.A.). He was elected a Fellow of the Royal Institute of British Architects (F.R.I.B.A.) in 1905.
In 1902 Bevan moved to South Africa to take up the position of Superintending Government Architect for the Transvaal. He returned to England in c.1905. In 1909 he moved to Canada and settled in Toronto, Ontario, where he was in partnership with Herbert E. Moore as Bevan & Moore until 1912 when he returned to England.
In 1923 and 1926 Bevan's address was given as "Penmare", Tavistock Road, Croydon, Surrey. He died in Bristol in March 1945.