 In March 1732, Dummer was elected a Fellow of the Royal Society 

In 1737, Dummer succeeded John Conduitt as MP for Southampton on the latter's death.Conduitt had left a daughter, Catherine, whose guardians sold the estate at Cranbury Park near Winchester to Dummer, as well as estates at Weston and Netley, near Southampton.Dummer continued to represent Southampton for four years until the 1741 election.