William Babington was born at Portglenone, near Coleraine, Antrim, Ireland. Apprenticed to a practitioner at Londonderry, and afterwards completed his medical education at Guy's Hospital, London, but without at that time taking a medical degree. In 1777 he was made assistant surgeon to Haslar (Naval) Hospital, and held this appointment for four years. He then obtained the position of apothecary to Guy's Hospital, and also lectured on chemistry in the medical school. He resigned the post of apothecary, and, having obtained the necessary degree of MD from the University of Aberdeen in 1795, was elected physician to Guy's Hospital.
William and Martha Elizabeth Babington were married before 1794, and had four sons and four daughters between 1794 and 1810. Babington died on 29 April 1833 and was buried at St. Mary Aldermanbury in London. He left a son, Benjamin Guy Babington, also physician to Guy's Hospital, and a daughter, Martha, who married the physician Richard Bright.