Dr. Anthony Askew, M.D., was born at Kendal, Westmoreland, in the year 1722. His father was Dr. Adam Askew, an eminent physician of Newcastle-upon-Tyne. He received his education at Sedbergh School, the Grammar School of Newcastle, and Emmanuel College, Cambridge. He took the degree of M.B. in 1745, and that of M.D. five years later. After leaving the University he went to Leyden, where he remained twelve months studying medicine, and then undertook an extensive tour on the Continent, during which he purchased a large number of valuable books and manuscripts. Dibdin says he was well known as a collector in most parts of Europe. In 1750, having finished his travels, Askew returned to Cambridge, where he practised for some time as a physician. He afterwards removed to London, where, aided by the patronage and support of his friend Dr. Mead, he soon acquired a considerable reputation, but he is better known as a scholar than a physician. Dr. Parr entertained a very high opinion of his attainments in Greek and Roman literature. Askew was a Fellow and Registrar of the College of Physicians, and also a Fellow of the Royal Society. He died at Hampstead on the 27th of February 1774.

Dr. Askew was an indefatigable collector, and filled his house from the ground floor to the attics with rare and handsomely bound books. The library, which numbered about seven thousand volumes, was extremely rich in early editions of the Greek and Latin classics, and its owner was ambitious that it should contain every edition of a Greek author. It comprised the first editions of the De Officiis of Cicero, the Natural History of Pliny, Cornelius Nepos, the History of Ammianus Marcellinus, the Fables of Æsop, the Works of Plato, and of many other Greek and Latin writers; the greater number of them being printed on vellum. A vellum copy of the Rationale of Durandus, printed by Fust and Schoeffer at Mentz in 1459; a first edition of the Teseide of Boccaccio, printed on vellum at Ferrara in 1475; a copy of the Greek Anthology, also on vellum, printed at Florence in 1494; Tully of Old Age, printed by Caxton, and a fine vellum copy of the Tewrdannck, were a few of the other notable books in the collection.

The printed books in the library were sold by Baker and Leigh at their auction rooms in York Street, Covent Garden, on the 13th of February 1775, and the nineteen following days. The lots were three thousand five hundred and seventy in number, and realised three thousand nine hundred and ninety-three pounds and sixpence. Among the purchasers at the sale were King George III., Louis XVI., King of France, Dr. Hunter and the Rev. C.M. Cracherode. The British Museum also acquired a considerable number of the books. The manuscripts, and the printed books with manuscript notes, were sold by Leigh and Sotheby in 1785. The sale took place on March the 7th and the eight subsequent days. There were six hundred and thirty-three lots, which produced eighteen hundred and twenty-seven pounds.

Askew was the author of a manuscript volume of Greek and Latin Inscriptions, copied by him during his travels in Greece and the Levant. The collection is preserved among the Burney Manuscripts in the British Museum.