Campbell was born in the Barony Parish of Glasgow in 1836, and grew up in Cathcart, a village in
Renfrewshire. He was educated in the parish school, and studied mathematics and physical sciences in
Glasgow. Some years later he studied medicine, and in 1867 was admitted to the
Royal College of Physicians,
Edinburgh, and the Faculty of Physicians and Surgeons, Glasgow. His health was never robust, which may have induced him to emigrate into South Australia, where he entered into partnership with Dr. H. Wheeler in
Adelaide sometime before February 1867. They were involved in the establishment of a homoeopathic dispensary in King William Street that offered its services free to the poor. He proved to be a very public-spirited citizen, and joined the committee of the
Society of Arts, and took a seat on the Board of Education, and was for a time its chairman, then on the committee established by the Education Act of 1875. He also held a seat on the Central Board of Health. For five years he was a member of the Adelaide University Council. He was a member of the Technical Education Board, whose report resulted in the establishment of the
South Australian School of Mines and Industries. was president of the
Literary Societies' Union, president of the
Institute of Architects, and chairman of the board of governors of the Museum, Public Library, and Art Gallery. He was, with
Lady Colton, the prime mover behind the establishment of the
Adelaide Children's Hospital. The Allan Campbell wing (now Campbell Ward) was named in recognition of his efforts. He was president of the Institute of Hygiene, an active supporter of the
St. John Ambulance Society, and helped found the
District Trained Nurses' Association. One of his last projects was the Queen Victoria Home for Convalescent Children at Mount Lofty, which was opened the week he died. ==Politics==