Allen was educated at Christ's Hospital and then at Trinity College, Cambridge, where he was a Classical scholar. He taught first at the School of Oriental and African Studies as a lecturer in Phonetics (1948-51) and then in Comparative Linguistics (1951-55), then held the position of Professor of Comparative Philology at the University of Cambridge until his retirement in 1982. His teachers and influences included N. B. Jopson, Harold Bailey and J. R. Firth, and R. H. Robins was a close colleague. He was elected a Fellow of the British Academy in 1971.
He was influential in the development of several important figures in British linguistics, including George Hewitt, John Lyons, John C. Wells, and Geoffrey Horrocks, who held Allen's former position as Professor of Comparative Philology. He was also influential in developing linguistics as a distinct discipline in 20th-century Britain, lobbying the General Board of the University of Cambridge to set up linguistics positions in the 1960s, and in helping to found the section for linguistics (subsequently renamed 'Linguistics and Philology') at the British Academy in 1985. The University of Cambridge has a prize named after him, awarded for distinguished performance by a linguistics undergraduate.
Lyons, John. William Sidney Allen 1918-2004. British Academy obituary. Contains photograph.