Quennell was the son of architect C.H.B. Quennell, and his wife, Marjorie Quennell who wrote extensively on social history. Educated at Berkhamsted Grammar School and at Balliol College, Oxford, he first practised journalism in London. While still at school some of his poems were selected by Richard Hughes for the anthology Public School Verse, which brought him to the attention of writers such as Edith Sitwell.
In 1922 he published his first book, Masques and Poems.This was followed by many other volumes, particularly his Four Portraits of 1945 (studies of Boswell, Gibbon, Sterne, and Wilkes), books on London and works on Baudelaire (1929), Byron (1934-35), Pope (1949), Ruskin (1949), Hogarth (1955), Shakespeare (1963), Proust (1971) and Dr Johnson (1972).
In 1930 he taught at the University of Tokyo. In 1944-51, he was editor of the Cornhill Magazine and from 1951 to 1979 founder-editor of History Today.
He published two volume of autobiography, The Marble Foot (1976) and Wanton Chase (1980). He was married five times and had two children, a daughter Sarah, from his third marriage and Alexander from his fifth. He received the CBE and was later knighted (in 1992).
Much of this biography is copied from Wikipedia's article on Quennell.
Quennell's primary contribution to Boswellian biography is a rather incorrect article on Boswell in Four Portraits (1945). It should be noted, however, that this was about five years before the general publication of Boswell's London Journal and before Boswell's private papers became widely available to others than collectors and specialist scholars. In 1973, he wrote Samuel Johnson - his Friends and Enemies.