Born at Lechlade in Gloucestershire on 20 September 1689, he was educated at Coxwell, Berkshire, and at Magdalen School in Oxford.
Having completed his course, he came to London to practise the civil law; but in 1710, on the death of his patron, Sir John Cook, dean of arches, he abandoned the legal profession and devoted himself to literary and antiquarian pursuits.
[2][3] Coxeter was a collector of old English plays, and allowed the Shakespearean editor, Theobald, to make use of them.
[1] Coxeter's manuscript collections were largely used in Theophilus Cibber's Lives of the Poets and in Thomas Warton's History of English Poetry.
In 1759, a four-volume edition of Philip Massinger's works appeared, "collated by Mr. Coxeter"; it was criticised by William Gifford.