She was born in St Ives, Cambridgeshire, the younger sister of Maria Gunning. They came to London together in 1751, and in the following year, Elizabeth married the James Hamilton, 6th Duke of Hamilton. When the Duke died in 1758, she married the John Campbell, later 5th Duke of Argyll. In 1770, again widowed, she was created Baroness Hamilton in her own right.