“A lie can travel half way around the world while the truth is putting on its shoes.”

Though widely quoted from his speech in the House of Commons, (1 November 1976) published in Hansard, House of Commons, 5th series, vol. 918, col. 976.; this is actually a very old paraphrase of a statement of the 19th century minister Charles Spurgeon: "A lie travels round the world while truth is putting on her boots." Even in the paraphrased form Callaghan used, it was in widely familiar, many years prior to his use of it, and is evidenced to have been published in that form at least as early as 1939.
Misattributed

Source: Moon Over Soho (2011), Chapter 13, “Autumn Leaves” (p. 277)

Source: Moby-Dick or, The Whale

Variant: I do know that the slickest way to lie is to tell the right amount of truth--then shut up.
Source: Stranger in a Strange Land

Memoirs of Cordell Hull (1948), 1:220
This is a variant of similar statements attributed earlier to Mark Twain, e.g., "A lie will fly around the whole world while the truth is getting its boots on." The oldest attribution (1831) is to Fisher Ames: “falsehood proceeds from Maine to Georgia, while truth is pulling on his boots”.

"Politics Getting Ready to Jell" <!-- p. 265 -->
The Illiterate Digest (1924)
Context: Every Gag I tell must be based on truth. No matter how much I may exaggerate it, it must have a certain amount of Truth.... Now Rumor travels Faster, but it don't stay put as long as Truth.

Source: The Principles of Uncertainty

Source: Ender's Game