Fanshawe was the fourth and youngest son of Sir Henry Fanshawe, of Ware Park, Hertfordshire and his wife Elizabeth Smythe, daughter of Thomas Smythe, of Ostenhanger Kent and was baptised at Ware on 12 June 1608. His father, who was Remembrancer of the Exchequer, died in 1616.George Edward Cokayne Complete Baronetage, Volume III, 1649-1664 1902
