Randolph was born in Bilston in 1886, the son of Walter Hugh and Annie Maria Delany. Randolph attended the Higher Grade School. In 1901 they were living at 94 Church Street, Bilston, along with Randolph’s siblings Alice Blanche Constance, Hugh Douglas, Walter Harry, Margery Mansell, Dorothy Philomena and Kathleen Mary. Randolph was a commercial clerk. In about 1904 he enlisted with the South Staffordshire Regiment (service number 6746), being promoted to Lance Corporal after three weeks. He served twice in South Africa. He became a sergeant-major. By 1911, the family were living at 94 Market Place, Church Street, Bilston, and Randolph was a merchant in the motor trade.
When war broke out, he volunteered and rejoined his regiment, in the 2nd Battalion, first entering the war on 12 August 1914. He took part in at least 16 engagements. In the course of these, he participated in hand-to-hand combat with the bayonet, and on one occasion a bullet went through his hat and another through his sleeve. He survived all unscathed. However, on 10 March 1915, he was killed in action at Givenchy. He was featured in the Midland Counties Express on 16 December 1916. He is remembered at the memorial at Le Touret, and appears on the Bilston Town Hall Ward Roll of Honour, as well as on the Roll of Honour for the Higher Grade School.