Harry Allen attended the University of Melbourne, graduating M.B. in 1876 and M.D. in 1878. He was appointed Demonstrator of Anatomy in 1880; lecturer in 1882, and in 1883, Professor of Descriptive and Surgical Anatomy and Pathology. In 1906, on the arrival of R.J. Berry, Professor of Anatomy, he became Professor of Pathology. He acted as honorary secretary for the second session of the Intercolonial Medical Congress in Melbourne, 1889, was Dean of the Medical Faculty from 1886, and president of the Royal Commission on the Sanitary State of Melbourne. He was also chairman of the Intercolonial Rabbit Commission. In 1890 he visited England and Europe, became the first colonial graduate registered there (he had done much to support the University's successful petition to permit such registration in Britain) and brought home up-to-date knowledge, leading to the establishment of bacteriology in the University. He was prominently associated with the establishment of the Institute of Tropical Medicine. He was a member of numerous medical bodies and associations and involved in the establishment of the Walter and Eliza Hall Institute.