According to this theory, which originates in a book by the eminent historian Renzo De Felice, the father of Fascism was not shot by Italian partisans but by the British secret services.
The reason was that Churchill had conducted an intimate correspondence with Il Duce before and during the war, and was worried that if he were captured and put on trial he could make some highly embarrassing disclosures.
Apparently Churchill had, among other things, tried to persuade Italy to stay out of the war by offering the Fascists sovereignty over Dalmatia, the Dodecanese Islands and other territories as a reward.
If you think that sounds extraordinary, just wait. The hottest items of the Churchill-Mussolini correspondence were contained in a black bag that Mussolini was carrying at the time he was killed, with his mistress and his closest intimates, by Lake Como on 28 April 1945, but somehow went astray in the confusion of the moment.
So determined was Churchill to recover the documents that he visited northern Italy in 1945 and 1946 to look for them, claiming to be holidaying with his easel and paints.
The Italian intellectual establishment has reacted with a mixture of stupor and scepticism about such disclosures but since they seem to come from Professor De Felice, it has felt obliged to take them seriously. Newspaper after newspaper has run replies to the professor, analysing the archives and recalling eyewitness testimony.
All have asked the same question: where is the proof? The only thing Professor De Felice has published so far is a book-length interview with a journalist, called Rosso e Nero (Red and Black), a taster of a mega- tome he plans to produce next year on the Italian civil war. There are no footnotes, and no documentary evidence.
``De Felice has almost certainly got something,'' concludes the historian and journalist Indro Montanelli, ``but I believe that either the famous exchange of correspondence does not exist, or is of little importance - certainly not worthy of a struggle for possession that could have come straight out of a film thriller.''
Foreign scholars have been rather less charitable. The Churchill scholar Andrew Roberts dismissed the theory as a ``sub-Hitler-diary story ... which flies in the face of everything we know about Churchill from the period''.
The Mussolini biographer Denis Mack Smith is equally sceptical but urges Professor De Felice to publish immediately any material he might have.
But maybe it is worth doing what all good historians should do, and returning to the source material. This is where the real surprise comes, because, in spite of everything that has been said and written about Professor De Felice, it is clear almost nobody has bothered to pick up Rosso e Nero and read it.
Virtually none of the elements of the conspiracy theory appears in it. Yes, Professor De Felice suggests that the British had reasons to see Mussolini killed but he says the secret services did no more than egg on the partisans, and certainly were not involved in the shooting themselves. Yes, he believes Mussolini's black bag included some select correspondence with Churchill, but he adds that it contains nothing of "absolutely definitive importance".
Instead of a brand-new theory about the death of Mussolini, it turns out that all we have is a new gloss on certain details. Professor De Felice makes no claim to have seen the Churchill-Mussolini correspondence, and only appears to believe it exists on the basis of testimony he has gathered from contemporary witnesses.
So where did the rest of the story come from? Sadly, it appears to have been entirely invented by the Italian press, with old conspiracy theories about the Churchill-Mussolini relationship spawning some spectacular conclusion- jumping over the De Felice book.
Suddenly the affair takes on the dimensions of a farce. Mr Montanelli began his learned piece in the Corriere della Sera with an admission that he had not read the book but merely seen extracts and commentaries in the press. A half-hour skim through Rosso e Nero would have saved him a lot of effort, and no doubt embarrassment as well.
Why has Professor De Felice kept silent? One can only speculate, although the fact that his book has shot to the top of the best-seller list might not be entirely without relevance.
One can perhaps conclude that the whole episode illustrates Italy's melodramatic fascination with one of the most traumatic moments in its recent history. A less kind moral to draw would be this: never take on trust anything you read in the Italian papers.