He was an MP for Cricklade, Wiltshire (1701–1702 and 1705–1713), Boroughbridge, Yorkshire (1713–1715), and Wallingford, then Berkshire (now Oxfordshire) from 1715-1719. He held the royal title of Master of the Household from 1708-1712. He was also a member of the Kit-Kat Club, a dining and gathering point for Whig supporters. He also had a reputation as a gambler and bon-vivant. He is buried at Little Wittenham Church, near Wallingford, in Oxfordshire (then Berkshire), in the village where the family had been based for over 170 years.
Many of Edmund's forebears had been parliamentarians, particularly representing Wallingford. William Dunch (1508-1597), auditor to the Mint for Henry VIII and Edward IV, represented Wallingford (1563), and was High Sheriff of Berkshire (1569-1570). It was William who bought the manor of Little Wittenham in 1552, which was the family seat. His son, Sir Edmund Dunch, represented Wallingford in 1571 and was High Sheriff of Berkshire (1586-1587). His son Sir William Dunch (1578-1611) represented Wallingford in 1603. He married Mary Cromwell in 1599, the daughter of Sir Henry Cromwell and aunt to Oliver Cromwell. It is believed that Mother Dunch's Buttocks, the variant name for the two rounded local hills Wittenham Clumps, is associated with her. William's brother Samuel (1592-1666) represented Wallingford in 1620. William's son, Edmund (1603-1678), was Governor of Wallingford Castle, and later became Baron Burnell of East Wittenham, though he lost this title at the Restoration (this being the only title conferred by the Protector and not confirmed by Charles II). He too represented Wallingford in 1627 and 1640, and was High Sheriff of Berkshire. Edward’s son Hungerford Dunch (1639-1680) was returned for Wallingford in 1660 but elected to serve for Cricklade. Hungerford's son was Edmund Dunch (1657-1719). Edmund, who had no sons, was the last Dunch to represent Wallingford. Edmund Dunch's daughter Arabella married Yorkshire politician Edward Thompson (1697-1742) and his daughter Harriet married Robert Montagu, 3rd Duke of Manchester.