has denied telling Boris Johnson he would "f*** him up" if he backed Brexit.
Lord Cameron, who served as Prime Minister and Foreign Secretary, made the threat as Mr Johnson considered whether to come out in favour of the EU.
And he channelled the late Queen Elizabeth II in saying "recollections differ" after Mr Johnson had claimed those were his "exact words".
The former Prime Minister said: "I find that hard to believe.
"What I do remember saying is, Boris, you've never backed Britain leaving the EU before, you've always said, let's reform it, let's change it. I said, why back it now when we got a better deal?"
Lord Cameron said he urged Mr Johnson to support plans to reform the EU, rather than quitting it.
He recalled: "You might not like my deal. You might think you can do better when you become prime minister, as you probably will in a few years time. But don't suddenly back something you've never backed before.
"I don't remember any language any fruitier than that. But you know, memories, recollections differ, as they say."
Mr Johnson revealed in Unleashed, that Lord Cameron also promised him a "top-five job" in the Cabinet if he vowed to back keeping Britain in the EU.
And the Brexit champion then described a phone call from Lord Cameron while he was in City Hall urging him to decide.
He wrote: "I was torn, I said. I wanted to back him, but over the years I had written hundreds if not thousands of articles attacking the undemocratic features of the EU. I felt I had to be consistent.
'This isn't about articles!' he spluttered. 'It's about... the future of the country!'
"Well, I said, we were agreed on that but I was still thinking of voting Leave.
"'If you do that,' he said - and these were his exact words - 'I will f--- you up forever.'"
Mr Johnson added: "I had to admit that the threat sounded serious. Did I want to be f***ed up? Forever? By a prime minister equipped with all the f***ing-up tools available to a modern government, and thousands of f***er-uppers just waiting to do his bidding?"
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