Allinson was born in the Hulme district of Manchester on 19 May 1858. He went to school in Lancaster and Manchester and at age fifteen began work as a chemist's assistant. With money he saved and financial help from his stepfather, he was able to attend the extramural medical school in Edinburgh, which was less expensive than the University medical school. He graduated as a Licenciate of the Royal Colleges of Physicians and Surgeons of Edinburgh (LRCP, LRCS) in 1879 at the age of 21 years. After assistantships in Hull and the East End of London he established his own practice in Marylebone in 1885. During the 1880s Allinson developed his theory of medicine, which he called Hygienic Medicine. In place of orthodox medicine, he promoted health through diet, exercise, fresh air and bathing.