Townshend was the eldest son of Sir Horatio Townshend, 3rd Baronet, who was created Baron Townshend in 1661 and Viscount Townshend in 1682. The old Norfolk family of Townshend, to which he belonged, is descended from Sir Roger Townshend (d. 1493) of Raynham, who acted as legal advisor to the Paston family, and was made a justice of the common pleas in 1484. His descendant, another Sir Roger Townshend (c. 1543–1590), had a son Sir John Townshend (1564–1603), a soldier, whose son, Sir Roger Townshend (1588– 1637), was created a baronet in 1617. He was the father of Sir Horatio Townshend.