A wealthy Hampshire landowner, with a reputed income of £20,000 a year, Dummer bought the house and estate of Cranbury Park from the executors of John Conduitt in 1737. He was returned for Southampton at a contested by-election in 1737, voting consistently with the Administration. On 19 Jan. 1741 his friend, Lord Hartington, wrote (to the Duke of Devonshire):
Dummer has no chance for coming in at Southampton and I believe will give it up, but we shall certainly have him in Parliament for some place or other.1B. B. Woodward & T. C. Wilks, Hist. Hants, ii. 99; VCH Hants, iii. 420; Chatsworth mss.
He stood again but was defeated. In 1747 he was brought in by the Administration for Newport. He died 6 Oct. 1765.