Entering politics, Dundas became Whig Member of Parliament for Greenwich at the 1832 general election and, having also become Deputy Lieutenant of Berkshire on 16 June 1834, he sat in Parliament until he stood down at the 1835 general election in favour of a fellow Whig. He was then given command of the first-rate HMS "Britannia", as flag captain to Admiral Sir Philip Durham who was Commander-in-Chief, Portsmouth, in 1836. He became Member of Parliament for Devizes in February 1836 in place of Sir Philip Durham who had stood down as Member of Parliament for that constituency. He then resigned his seat in Parliament when he became Clerk of the Ordnance on 21 March 1838. He was appointed a Companion of the Order of the Bath on 25 October 1839.