Mr Johnson had claimed those were the Tory peer's "exact words" as he considered whether to come out in favour of the EU.
Former PM Lord Cameron 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'. I said, 'Why back it now when we got a better deal?"."
Deal
He said he urged the former Mayor of London to support plans to reform the EU, rather than quitting it.
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