William Alcock, a tin smith and sheet metal worker, emigrated to the Cape Colony in 1871 and settled in Walmer, now a suburb of Port Elizabeth. He was married to Emily Nimmo, with whom he had two sons and a daughter. In 1890 he and his youngest brother Edwin opened a sheet metal workshop. In 1899 he became the first mayor of Walmer.
From about 1884 Alcock participated in various scientific activities. His skills and interests pertained mainly to instrumentation, particularly in microscopy and photography. He joined the Eastern Province Naturalists' Society (1882-1923) in July 1884 and in December of that year, at the society's conversazione, demonstrated his lime light microscope. That same year he also gave demonstrations on bird taxidermy. During 1886 he selected and brought out a dissecting microscope from England to be used at the society's meetings. He served as honorary treasurer in 1887 and 1888, and as a member of the society's management committee in 1891.
In July 1891 Alcock chaired two meetings in Port Elizabeth to form the Port Elizabeth Amateur Photographic Society, and was elected its first president. During 1896 the wonders of roentgen ray (X-ray) photography were first demonstrated all over the world, following W. Roentgen's discovery of the rays in November 1895. One of the earliest roentgen ray photos produced in South Africa was taken on 13 August 1896 in Port Elizabeth, by Albert E. Walsh*, who was then president of the Port Elizabeth Amateur Photographic Society. Alcock acted as his assistant, while a reporter of the Port Elizabeth Telegraph witnessed the event.
In 1900, while on a visit to Britain, Alcock bought a Benz Velo motorcar and brought it to Port Elizabeth - the first motor vehicle in the city. Two years later he made the first trip ever by motorcar from Port Elizabeth to Grahamstown. In 1903 he became the first chairman of the Eastern Province Automobile Society.