He was the son of David Webster (died 1801), a West India merchant in London, initially called David Wedderburn, who changed his name in accordance with the will of his business partner James Webster (died 1789) with an interest in the Richmond Vale estate in Jamaica (the family relationship being that James Webster was a son by a second marriage of David Wedderburn's maternal grandmother Beatrix Proctor): he was in early life known as James Wedderburn Webster.