Elizabeth Altham married Arthur Annesley, 1st Earl of Anglesey, second Viscount Valentia and first Earl of Anglesey, whose second son, Altham Annesley, was created in 1680 Baron Altham of Altham, with limitation in default of male issue to his younger brothers. His only son dying in infancy, the title devolved upon the younger branch of the Annesley family, who subsequently succeeded to the earldom of Anglesey. The earldom lapsed in 1771, when the English House of Lords decided against the legitimacy of the last claimant.
