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Grenville was the son of Richard Grenville born into a family of politicians, one of his elder brothers was Earl Temple, another a government minister, another was Lord of Trade and Cofferer of the Household, while another brother George Grenville rose to become Chancellor of the Exchequer of William Pitt and then Prime Minister himself 1763–1765.
Henry Grenville was Governor of Barbados from 1746. He was appointed British ambassador to the Ottoman Empire in Constantinople on 1 May 1761, but did not arrive until 21 February 1762. He was recalled only three years later on 31 May 1765, during the reign of Sultan Mustafa III.
He left Turkey to return to England on 13 October 1765 to become Commissioner of Customs before retiring to Bath, where he died in 1784.
His daughter Louisa married the statesman and scientist Charles Stanhope, 3rd Earl Stanhope.
- Turkey: Its History and Progress – the journals and correspondence of Sir James Porter. London, Hurst and Blackett. 1854.
- Wood, Alfred C. (1935). A History of the Levant Company. London.