Arthur was born in Bedlington, around 1882, to Thomas and Hannah Dunn. He was educated at Newcastle Royal Grammar School before going on to study medicine at the College of Medicine in 1898, from where he graduated in September 1903 (M.B., B.S.).
Upon qualifying as a doctor, Arthur was employed at the Old Infirmary as an Accident Room House Surgeon and later as a House Surgeon. He later went on to serve as the House Surgeon of the Eye Department. From 1906 Arthur worked as the Resident Medical Officer at the Fleming Memorial Hospital for Sick Children, until he was appointed as Resident Medical Officer to the Newcastle Dispensary in 1908. Arthur filled this role for 5 years, before starting a private practice in 1913. He was married to his wife Ann in the same year.
Arthur served in the 1st Northumbrian Field Ambulance between 1910 and 1914, but resigned his commission in order to focus on his newly established private practice. In June 1915, he joined the staff of the Northumberland War Hospital as a civil medical practitioner, before eventually being commissioned into the Royal Army Medical Corps in April 1917.
Arthur died on the 5th September 1917, less than 6 months after re-joining the Army.