He was the son of Sir George Cooke, a barrister who became chief prothonotary in the Court of Common Pleas, and his wife Anne, daughter of Edward Jennings, Member of Parliament for East Looe.
He had the life appointment as chief prothonotary, from 1732, and also inherited the family estate, Harefield in Middlesex.
[1][2] In 1742 Cooke entered parliament, as member for Tregony, supported by Hugh Boscawen, 2nd Viscount Falmouth.
Initially a Tory, he became a follower of William Pitt the elder in the later 1750s.
[1] Cooke married Catherine, daughter of Sir Thomas Twisden, 4th Baronet, in 1735; they had seven sons.