The Dalston family were descended from Hubert de Vaux, Lord Gillesland and Baron of Dalston about the time of the Norman Conquest.
Sir John Dalston and his son Sir George Dalston (father of the first Baronet) both served as High Sheriff of Cumberland during the reign of James I.
The first Baronet was Member of Parliament for Carlisle 1640-44 and High Sheriff of Cumberland in 1665.
The second Baronet, who was knighted in 1663, prior to his succession, served as High Sheriff of Cumberland in 1661.
The Baronetcy was extinct on the death of the fourth Baronet in 1765.