He studied at Guy"s and Saint Thomas"s Hospitals, and became licentiate of the Society of Apothecaries in 1825, member of the Royal College of Surgeons in 1828, and fellow in 1852.
Dunn was a phrenologist and associated at the Westminster Medical Society with others (John South Streeter, Forbes Winslow and Edward Wright). He was Fellow of the Royal Medical and Chirurgical Society, along with the phrenologists Thomas Ignatius Maria Forster and Joseph Moore. He was also Fellow of the Obstetrical Society, the Ethnological Society of London, and of the Medical Society of London.
And was for many years treasurer to the metropolitan counties branch of the British Medical Association.