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. He was the author of many works, the first of which is a poem entitled Sighs on the Death of Queen Anne, printed probably about the time of her death in 1714. Two years afterwards he printed an Exercise on the Creation, and a Hymn to the Creator of the World, being an attempt to show the beauty and sublimity of the Holy Scriptures, 1716, 8vo. In 1721, being then curate of King's Clifton in Northamptonshire, he issued proposals for printing the History and Antiquities of his native town, a work which was published in 1727, in folio, under the title of Academia tertia Anglicana, or the Antiquarian Annals of Stamford, in Lincoln, Rutland, and Northamptonshires, inscribed to John duke of Rutland. This work was hastened by an Essay on the Ancient and Present State of Stamford, 1726, in 4to, written by Francis Hargrave, who, in his preface, mentions the difference which had arisen between him and Mr Peck, on account of his publication having forestalled that intended by the latter. Mr Peck is also very roughly treated on account of a small work which he had formerly printed, entitled the History of the Stamford Bull-running. Mr Peck had before this time obtained the rectory of Godeby, near Melton, in Leicestershire, the only preferment he ever enjoyed. In 1729, he printed, on a single sheet, Queries concerning the Natural History and Antiquities of Leicestershire and Rutland, which were afterwards reprinted in 1740; but although the progress he had made in the work was considerable, yet it never made its appearance. 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 Manners, and was followed, in 1735, by a second volume, dedicated to Dr Reynolds, bishop of Lincoln. In the year 1735 Mr 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, a great number of them not mentioned in the three former catalogues; with references after each title, for the more speedily finding a further account of the said discourses and their authors in sundry writers, and an alphabetical list of the writers on each side. In 1739 he edited Nineteen Letters of the Reverend Dr Henry Hammond, author of the Annotations on the New Testament, written to Mr Peter Stainmough and Dr Nathaniel Angelo, many of them on curious subjects. These were printed from the originals, communicated by Mr Robert Marsden, archdeacon of Nottingham, and Mr John Worthington. The next year, 1740, he produced two volumes in quarto, one of them entitled 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. The other contained 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 Shakspeare, by the editor; besides a variety of other pieces, which it would be tedious to enumerate. These were the last publications which he gave the world. When they appeared, however, he had in contemplation no less than nine different works; but, from some cause not explained, none of them was ever made public. He concluded a laborious, and, it may be added, useful life, wholly devoted to antiquarian pursuits, on the 13th of August 1643, at the age of sixty-one years.