Abercromby was a grandson of Henry Dundas, 1st Viscount Melville, and nephew of the 2nd Viscount, first lord of the admiralty in Lord Liverpool’s administration and manager of its Scottish interests. His army career was largely nominal. He was only 19 at the time of the 1820 general election, when his father gave his decisive support in Clackmannanshire to his cousin, Robert Bruce of Kennet, as a locum for him. He duly took the seat in July 1824, when he was reckoned to have made ‘an eloquent and impressive’ speech of thanks.
Abercromby was returned unopposed for Clackmannanshire at the general election of 1830.
He supported the successful Liberal at the 1832 general election in the new constituency of Clackmannan and Kinross.
