The eldest son of Peter Warburton of Hefferston Grange, Cheshire, grandson of Sir Peter Warburton (d. 1550) of Arley in the same county, by Magdalen, daughter of Robert Moulton of St. Alban's, Wood Street, London, auditor of the exchequer in the reign of Elizabeth, he was born on 27 March 1588. At Oxford, where he matriculated at Brasenose College on 11 May 1604, he graduated B.A. on 22 November 1606.