William Edmunds, son of the architect William Edmunds and his wife Ann, born Burn, was educated at the King's School, a prestigious boarding school in Canterbury, Kent, from 1839. He qualified as a member of the Royal College of Surgeons (MRCS), London, in 1852. After some time as a military surgeon he was licensed to practice in the Cape Colony in August 1854 and settled in Grahamstown during the same year. His medical appointments during the next eight years included that of medical officer to Albany Hospital, surgeon to the Grahamstown Volunteers, and surgeon to the Katberg Convict Station.
On 3 July 1855 Edmunds was one of the five medical men who founded the Grahamstown Medico-Chirurgical Society, the others being W.G. Atherstone*, G.A. Hutton*, R.M. Armstrong*, and A.L. McDonald*. The meeting was held at Edmunds's house in Bathurst Street. The interests of members stretched far beyond medicine, however. A museum collection was soon started, which developed into the Albany Museum. At the end of the year the society was renamed the (Grahamstown) Literary, Scientific and Medical Society, to accomodate a wider membership. Its proceedings and many of the papers read before it were published in the Grahamstown Journal. For several years Edmunds played an active role in the society, particularly in its efforts to disseminate knowledge and stimulate an interest in science. During the first nine months many of the meetings were held at his house, while he also provided room in his house for the museum collection. When the society obtained its own premises in April 1856 he was presented with "a very handsome and valuable" Atlas of physical geography in recognition of these services. He was a member of the society's management comittee, and of its museum committee from the inception of these committees in 1855. During 1858 he and W.G. Atherstone arranged the collection of mammals and birds. His donations to the museum included the crania of a gnu and a bushbuck.
Edmunds read his first paper before the society on 28 August 1855, on "Anaesthesia and anaesthetic agents", with particular attention to the administration and effects of chloroform. Anaesthetics, which he described as "one of the greatest blessings science has yet bestowed on mankind", had been used at the Cape for only eight years at the time. Subsequent papers included "On mechanisms of the human frame" (February 1856); "On the anatomy and physiology of the ear" (April 1857); and "Our food: animal and vegetable" (May 1858). The latter dealt with the constituents of food and the effects of diet on health, and was published in the Eastern Province Monthly Magazine (Vol. 2, pp. 575-582, 631-639). As part of the society's efforts to stimulate public interest in science, Edmunds presented various lectures and classes. For example, in January 1856 he and Dr Hutton announced that they would present bi-weekly classes in physiology. During 1857 he presented a series of five lectures on "Elementary chemistry", which included topics such as heat and light, now classified under physics. In the same year he delivered several lectures on "The chemistry of the seasons", dealing with biological changes and including topics such as the effects of light and reactions taking place in the air. These lectures were published in the South African Agricultural Register. In November 1857 he spoke on the zoological specimens in the society's museum. And during 1860 he presented a lecture on "Chemistry applied to the arts".
Edmunds's other activities included serving on the first executive committee of the Eastern Province Agricultural Association, founded in Grahamstown on 9 November 1855. In June 1862 he left Grahamstown for Robben Island, which contained a leper colony and convict station, and was home to both chronic and psychiatric patients. After acting as superintendent in the absence of Dr. Minto he was appointed surgeon superintendent on the island at the end of 1863, and from 1866 also as visiting magistrate to the convict station. He died in 1872 and was buried in the cemetary on the island.
Edmunds married Georgina Jane Harrington in London in 1854. His father died in a lunatic asylum in 1847. His elder sister, Christiana, famously committed a mass poisoning in Brighton in 1871 and spent the rest of her life in Broadmoor Lunatic Asylum. His younger brother, Arthur, also died in an asylum.