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His father, William Harcourt Isham Mackworth (1806—1872), a younger son of Sir Digby Mackworth, the 3rd Baronet, took the additional surname Dolben after he married Frances, the heiress of Sir John English Dolben, the 4th Baronet.
He had four daughters by his first marriage, and one son, Thomas, by his second, who succeeded him in the baronetcy.
Strickland was the eldest son of Sir William Strickland of Boynton, a Yorkshire landowner and Member of Parliament, and his wife Elizabeth Palmes.
Sir William Strickland, 1st Baronet (c. 1596–1673), Member of Parliament during the English Civil War