William Greenstock, a Church of England clergyman, was ordained priest in 1855. That same year he was sent to the Cape Colony as a missionary of the Society for the Propagation of the Gospel. He was stationed in the Eastern Cape at St Luke's Mission (1855-1858), the East London Mission (1858-1859) and the St Mathew's Mission at Keiskammahoek (February 1859-1870). From 1870 to 1875 he was a curate at St Mary's church in Port Elizabeth. During his years in the Eastern Cape he proved a gifted clergyman and a successful teacher. He translated into English various essays written by the more advanced students at St Matthews Mission School, Keiskamma Hoek, and the originals with the translations were published as Kafir essays and other pieces (Grahamstown, 1861). From about 1872 he was president for some years of the Port Elizabeth Mechanics' Institute (founded in 1849), an organisation concerned mainly with adult education and upliftment. He also served on the committee of the town's public library.
In 1875 Greenstock moved to Durban where he befriended Thomas Baines* and ministered to him when he died in May that year. That same month Greenstock left Durban and travelled to Pretoria, and in July on to the farm Eersteling (north-east of Potgietersrus) where Edward Button* was working the first Transvaal gold mine. In August Greenstock travelled to Woodbush (later renamed Houtbosdorp) and returned to Eersteling. In January 1876 he left for Pilgrim's Rest and the next month visited Mac Mac. His journey ended temporarily at Lydenburg, but he soon moved on to Pretoria. From Lydenburg he requested the government of the South African Republic (Transvaal) in February 1876 to be recognised as a marriage registrar. His "Notes of travel", describing the journey from Durban to Lydenburg, was published in the form of ten articles in The Mission Field (London) in 1876. The next year he described his journey from Lydenburg to Pretoria in the same journal. In the Transvaal book almanac (Jeppe, 1877) he was listed as minister of the English Episcopal Church of the goldfields.
While in the northern Transvaal Greenstock collected plants. His specimens went to the British Museum (Natural History) and though all are said to have been collected at Pilgrim's rest it is evident that he collected elsewhere as well. The species Crossandra greenstockii and Ipomoea greenstockii were named after him.
Greenstock later returned to Natal, where he was stationed from 1879 to 1885. His wife, Frances E. Cotterill, with whom he had about 10 children, died in 1881. In 1886 he was engaged to be married to Virginia Levinia Isitt, the first headmistress of the Collegiate School for Girls in Port Elizabeth, but circumstances prevented the marriage. In 1884 he was involved in the establishment of a school at Springvale Mission, east of Ixopo. He resigned from his missionary work in 1885 and lived in England for some time. In 1894 he started work again, this time in Thailand. He was probably the same person as William Greenstock who published A primer of Greek exercises... (London, 1895) and Single term Latin readers.... (London, new edition, 1923).