He was the fifth son of Sir Thomas Barrett-Lennard, 1st Baronet, and Dorothy St. Aubyn and a grandson of Baron Dacre of Belhus in County Essex, England.
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Thomas Dacre, 4th Baron Dacre of Gilsland (1527/1530- 1 July 1566), married firstly Elizabeth Neville, and secondly Elizabeth Leyburne, by whom he had five children, including George Dacre, 5th Baron Dacre of Gilsland, 4th Baron Greystoke, and Anne Dacre, later Countess of Arundel (21 March 1557 – 19 April 1630).