Physician and surgeon, he trained at the Middlesex Hospital and went to Ipswich as a house surgeon in 1921. After periods in the Norfolk and Norwich Hospital and the Middlesex, he returned to Ipswich, where he spent the rest of his life, first as a GP and, from 1939, as consultant surgeon at the Ipswich and East Suffolk Hospital. In 1952 he became a Fellow of the international College of Surgeons and from 1955 to 1961 was senior consultant surgeon.
A lifelong Methodist, he and his wife Elsie (a theatre sister before their marriage and a strong supporter of overseas missions) were members of Museum Street church and are remembered locally as extremely generous and supportive, especially of young people. During World War II they became close friends of Dr. Harold Roberts. As a result, Arthur Hill served on a number of connexional committees and was a British representative to a succession of World Methodist Conferences in 1951, 1956, 1961 and 1966. He declined to be nominated as Vice-President of the Conference on the grounds that the demands of his medical work were paramount.
He was largely instrumental in the establishment of the Norwood MHA in Park Road. The acquisition of the property arose through his friendship with the Bishop of St Edmundsbury and Ipswich, wo lived in a neighbouring house. Arthur Hill proposed an exchange of the respective properties, donating the former bishop's residence to MHA.