McKay (1880-1948) was born and raised in Jamaica. He emigrated to the United States in 1912 to attend college. He became active in radical politics and wrote "If We Must Die" in reaction to race riots that swept America during the 1919 "Red Scare." The poem was first published that same year in the July issue of The Liberator, a left-wing magazine edited in New York by Max Eastman.
In an article published in the September 2003 issue of Notes & Queries, Lee M. Jenkins traced the history of the claim that Churchill quoted McKay's poem during the Second World War. According to Jenkins, the story started after the war with such black writers as Melvin B. Tolson, Kamau Brathwhite and Arna Bontemps. Variously, Churchill is supposed to have cited the poem in speeches made in the House of Commons or to the United States Congress, or both. This urban legend focused on the supposed irony of a famous white leader quoting a black poet.
In fact, there is no evidence that Churchill cited the poem in any speech. No reference can be found in Hansard (Parliamentary Debates) or the Congressional Record. Nor could the quote be verified by the Churchill Archives Centre or The Churchill Centre. The author Gore Vidal opined that it is very unlikely Churchill, assuming he knew the poet's identity, would have quoted the lines before a Congress controlled largely by Southern racists.
Probably, the confusion stems from the fact that the poem "If We Must Die" certainly sounds like the sort of things Churchill did say during World War II. It is even possible that Churchill was familiar with the words, since in 1919 McKay left the U.S. for London, where he worked for Sylvia Pankhurst's radical newspaper, The Worker's Dreadnought, and Churchill was well known for reading papers across the political spectrum.
Still, in the absence of any documented evidence, the story must be regarded as a myth.