Duff Cooper was a diplomat who had held several top level posts during the war. In 1950, he published a spy novel, Operation Heartbreak. The key plot device was floating a corpse into Spain with false documents to deceive the Germans. Cooper had come up with the idea on his own, but naturally, many of those concerned with Mincemeat (including Germans and Spaniards) became concerned and started talking. The 'flap' attracted the attention of the British press and wild rumours began to circulate. At this point, the British security services decided that the best response was to publish the story of Mincemeat, which would not compromise any other secrets. Ewen Montagu took a weekend off from his busy legal practice and wrote the book The Man Who Never Was. It was an immediate best-seller and was made into a movie of the same name two years later. The movie added some fictitious elements for drama, such as a German agent in London verifying the background of "Major Martin", with Montagu and his colleagues one step ahead of him.
In 1977, Montagu published a second book, Beyond Top Secret ULTRA, in which he recounted his secret war work. It could not be revealed earlier, as it involved both Ultra and the Double Cross System. In chapter 13, he gives a short version of the Mincemeat story, including some details not in The Man Who Never Was.
As noted/implied above, anything written about WWII prior to that point in the '70s when Ultra could be talked about has to be taken with a grain of salt/suitable adjustments.