Torkington was educated at Clare College, Cambridge. He became Fellow in 1768. He was ordained a priest in the Church of England in 1771. He held incumbencies at Little Stukeley, Patrington, Stapleford and Teigh. Webb was Vice-Chancellor of the University of Cambridge between 1783 and 1784.
- 'Births, Deaths, Marriages and Obituaries' The Hull Packet and Original Weekly Commercial, Literary and General Advertiser (Hull, England), Tuesday, July 18, 1815; Issue 1499
- Alumni Cantabrigienses: A Biographical List of All Known Students, Graduates and Holders of Office at the University of Cambridge, from the Earliest Times to 1900, John Venn/John Archibald Venn Cambridge University Press > (10 volumes 1922 to 1953) Part II. 1752-1900 Vol. vi. Square – Zupitza, (1954) p210
- Full List of Vice-Chancellors of the University of Cambridge
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