According to the conspiracy the Japanese were allowed to attack so that America could be dragged into the war.
A central plank of the conspiracy was a telegram from Churchill to Roosevelt said to be in a secret file the government had withheld from the Public Record Office. That file has now been released. There is no telegram and it seems there probably never was.
What is in the file is fascinating - the story of a Scottish Lord suspected of leaking information to the Japanese in 1940. This explains why the file was withheld for so long.
There are two versions of the great Pearl Harbor conspiracy theory. In the first, Churchill informed Roosevelt of Japan's intent but the two leaders agreed to sit on the information.
The second version - that Churchill knew of the Japanese plan but did not tell Roosevelt - was most forcefully advanced by the British authors James Rusbridger and Eric Nave in their 1991 book Betrayal at Pearl Harbor. They claimed that the British had broken the codes of the Japanese Fleet and knew that the Japanese would steam east and attack the American base.
This version was given credence because Captain Nave had broken the Japanese naval cipher JN-25 in 1939. James Rusbridger was a former MI6 courier who had become a self-styled expert on intelligence matters. He was also the cousin of MI5's Peter Wright of Spycatcher fame.
What is certain is that on 7 December 1941 the Japanese attacked Pearl Harbor, the American military base on Hawaii, sinking 19 warships of the United States Pacific Fleet, destroying 120 aircraft and killing 2,400 servicemen.
According to conspiracy theorists, Churchill was desperate to get Americans into the war to help the beleaguered British. This is undoubtedly true. The next strand is that Roosevelt was sympathetic but could not bring the United States into the war without a pretext. It is certainly true that Roosevelt was sympathetic and Pearl Harbor swung the American people behind him for war.
Whichever conspiracy you take, both versions say that the key moment is 26 November 1941 and involves a telegram. Rusbridger and Nave maintained that Churchill knew by then of the forthcoming Japanese attack. The question is - did Churchill tell Roosevelt? They alleged there is one piece of correspondence that has never been seen. That would provide the answer.
Rusbridger and Nave said on that night Churchill sent two telegrams to Roosevelt. The first sent at 3.20am (London time) has long been publicly available. It refers to American diplomatic negotiations with the Japanese to stave off war. It ends: "There is only one point that disquiets us. What about Chiang Kai-shek? Is he not having a very thin diet?"
Rusbridger and Nave commented that "Churchill's sudden interest in China was surprising and not particularly convincing," implying that Churchill was playing a game with Roosevelt.
But it is the second telegram that the two authors believed was crucial. "Sometime later on 26 November, Churchill's private secretary, Anthony Bevoir, sent by hand to the American Embassy a second message to be transmitted to Roosevelt," they said in their book.
Antony Best, a historian at the London School of Economics and author of book on Pearl Harbor said: "I was very doubtful that the second telegram existed. I think it is just one of those mistakes of history. I have never found any evidence that there was a conspiracy and I have looked high and low."