William Alexander Greenhill (1 January 1814, Stationers' Hall, London – 19 September 1894, Hastings) was an English physician, literary editor and sanitary reformer.
William Alexander Greenhill was the youngest of three sons of George Greenhill, treasurer of the Stationers' Company. He was educated at Rugby School under Thomas Arnold: a favourite pupil of Arnold, he later married Arnold's niece Laura Ward. At Rugby he befriended A. H. Clough, W. C. Lake, A. P. Stanley and C. J. Vaughan; he went on to Trinity College, Oxford, where he took no arts degree but (studying medicine at the Radcliffe Infirmary and Paris) graduated M.B. in 1839 and M.D. in 1840.
Greenhill was appointed physician to the Radcliffe Infirmary in 1839. A "pioneer in the cause of sanitary reform, in the days when sanitary reform was thought a crazy fanaticism", he first wrote on Oxford's public health and mortality for the Ashmolean Society, after a cholera outbreak in Oxford.
In 1840 he hosted Richard Francis Burton in his house, encouraging the young student to study the Arabic by introducing him to the Spanish scholar Don Pascual de Gayangos. At the time Greenhill, who lived in John Henry Newman's parish, was serving as Newman's churchwarden; he came to know Pusey, and other leaders of the Oxford Movement. Other Oxford academic friends included Charles Page Eden, William John Copeland, Charles Marriott, J. B. Morris and James Bowling Mozley. A political liberal, Greenhill actively supported William Ewart Gladstone's election as MP for the university in 1847. Like other university liberals, however, he was later discomfited by Gladstone's direction in the 1880s: he did not vote liberal in 1885 (fearing disestablishment of the Church of England) or 1886 (objecting to the Home Rule programme.)