Connolly, a Londoner of Irish descent, was an editor of the New Statesman and a novelist, an accomplished literary critic, essayist, and a collector.

Connolly's passion for collecting books drove him into debt and as a result, he sold many of his fine editions and collections over the years as the need arose. Tellingly, Connolly himself joked that the memorial for his death should take place at Sotheby's, where cantors would perform a "sung bibliography" and chant a "wants list".

Connolly was for many years a weekly reviewer for the Sunday Times. In 1939, with Spender, he founded the literary magazine Horizon (1930 - 50), and through it, he exercised considerable critical influence.

His only novel, The Rock Pool (1935) is a satiric extravaganza describing the adventures of an artistic expatriate colony on the French Riviera.

His works include Enemies of Eden (1938), critical essays. The Unquiet Grave (1945), published under the pseudonym of Palinurus, consists of aforisms, reflections, etc. Both received significant praise, but he is best known as a book reviewer with classical taste.