Greville was the third son of Francis Greville, 5th Earl of Warwick, by his wife Frances Evelyn (granddaughter of 3rd and last Viscount Maynard). He was a Lieutenant in the Royal Air Force, and served in WWI. On 19 February 1918, he married Dora [d. 1957], daughter of Edward Pape of Moor Hall, Battle, Sussex (also of London). They had a daughter, Felice.