Francis, a laborious and learned antiquary, was born at Stamford, in Lincolnshire, on the 4th of May 1692, and educated at Cambridge, where he took the degrees of Bachelor and Master of Arts. After several unsuccessful flights in poetical composition, he, in 1727, published in folio his Academia tertia Anglicana, or the Antiquarian Annals of Stamford, in Lincoln, Rutland, and Northampton Shires, inscribed to John, Duke of Rutland. Peck had before this time obtained the rectory of Godeby, near Melton, in Leicestershire, the only preferment he ever enjoyed. In 1732 he published the first volume of Desiderata Curiosa, or a collection of various scarce and curious pieces relating chiefly to matters of English history. This volume was dedicated to Lord William Murray, and was followed, in 1735, by a second volume, dedicated to Dr Reynolds, Bishop of Lincoln. In the year 1735 Peck printed a complete catalogue of all the discourses written for and against Popery in the time of King James II., containing in the whole an account of 457 books and pamphlets, with references after each title, and an alphabetical list of the writers on each side. After editing Dr Hammond's Letters in 1739, he next year produced Memoirs of the Life and Actions of Oliver Cromwell, as delivered in Three Panegyrics of Noll, written in Latin, and supposed to have been composed by John Milton, Latin Secretary to Cromwell; also, New Memoirs of the Life and Poetical Works of Mr John Milton, with an Examination of Milton's Style, and Explanatory and Critical Notes on different passages in Milton and Shakespeare, together with sundry poetical effusions, "in imitation of Milton." At his death in 1743, this singularly industrious author is said to have had no fewer than nine different works in contemplation.