Anne was one of the two daughters of Dr Richard Huck-Saunders (born Richard Huck) and his wife, the former Jane Kinsey. Her great-uncle was Admiral Sir Charles Saunders. Her elder sister Jane became Countess of Westmorland.[3] Through the admiral, his wife's maternal uncle, Dr Huck-Saunders and his wife acquired a sizeable inheritance, which passed to their daughters.[4]
Anne married the future viscount on 29 August 1796, when he was an MP. He inherited the viscountcy in 1811, making her a viscountess. The couple had six children, including:
Reverend Hon. Charles Dundas (1806-1883), who married Louisa Maria Boothby and had seven children, including Robert Dundas, 5th Viscount Melville, and Charles Saunders Dundas, 6th Viscount Melville