His son, the second Baronet, also represented Thirsk as well as Hedon in the House of Commons.
His son, the third Baronet, sat as a Member of Parliament for Harwich and Thirsk and served as a Lord of the Admiralty from 1730 to 1741.
He was succeeded by his nephew, the fourth Baronet, who notably served as Consul-General in Lisbon.
His son, the sixth Baronet, was a Fellow of the Royal Society and a Member of Parliament for Thirsk.
In 1837 he assumed by Royal licence the surname of Russell after Frankland on inheriting Chequers Court in Buckinghamshire from his kinsman Sir Robert Greenhill-Russell, 1st Baronet, of Chequers Court.