Born in 1884 or 1885 he took second-class honours in the Natural Sciences Tripos, part I, 1906, from Trinity College, Cambridge. After qualifying in 1909, Archer was a house surgeon at St Bartholomew's Hospital. He was for a time visiting surgeon at Beverley Road Infirmary, Hull and served as a temporary surgeon in the Royal Navy during the first world war. For the rest of his life he was in general practice in Hampshire, living at the White House, Hythe. Archer died suddenly, aged 71, on 17 June 1956 at his home at 9 Westport Road, Wareham, Dorset. He was survived by his wife.