The son of George Jepson, surgeon, of Gainsborough, Lincolnshire; he studied at St Bartholomew's Hospital, where he was House Surgeon under Earle. He practised throughout his life at Durham, where he was in partnership with William Green and later alone. He was Medical Officer to the Sherburn Hospital, and after its reorganization, Surgeon to the County Hospital. He was also Medical Officer to the Penitentiary. When the Public Health Act was brought into operation, he became the first Medical Officer of Health. In 1889 he retired to Scarborough and died there in December, 1895, or January, 1896. His eldest son, Edward Jepson, MD, who had succeeded to his father's practice, was then Mayor of Durham.