His grandfather Sir William Pope of Wroxton Abbey, near Banbury, was created Earl of Downe in the kingdom of Ireland, and died on 2 July 1631.
On 26 November 1638 he married his guardian's daughter Lucy, and on 21 June 1639 matriculated as a nobleman at Christ Church, Oxford; but he offended against academic discipline, and before 13 March 1641 he left the university.
The sequestration was finally discharged on 18 April 1651, after he had sold, under powers obtained by a private act in 1650, all his lands, except the manors of Cogges and Wilcote, Cubberley, which he held in right of his wife, and Enstone, with the adjacent townships.
Just before Downe's death his only child, Elizabeth (born at Cogges 15 April 1645), married Sir Francis Lee, 4th Baronet.
Her second husband was Robert Bertie, 3rd Earl of Lindsey; and the Enstone property descended through her to the Viscounts Dillon.