Mr Johnson has taken the tougher line, even refusing to rule out suspending Parliament to force through a no-deal against the wishes of MPs.
"If a male prime minister's voice had broken up, it would have been said "what great patriotism, they really love their country".
"Boris commands a significant majority in terms of the parliamentary support and it is important that the next PM restores a collective vision and responsibility in this Government and I feel Boris Johnson is best placed to appoint the strongest Cabinet possible to deliver in this monumental task that we face".
In an interview with the BBC's Andrew Neil, the Foreign Secretary said he was not prepared to make the commitment when it was clear Parliament could block it.
May underscored she had done all she possibly could to try to get her Brexit deal approved and did nothing to hide her frustration with the fact that some of her most strident opponents on Brexit are those now backing Johnson.
She's also brandishing her credentials because she's still not assured of that job remember, and there's still an very bad lot to play for, so she's really just trying to play up her credentials in terms of defending the Brexit deal that Barnier supposedly negotiated, and which has led to the downfall of our existing Prime Minister.
Clark told Sky News on Friday that the disruption of a no-deal departure would lead to job losses.
But the former foreign secretary insisted his comments in the debate had been "misrepresented" and denied withholding his backing.
But in tonight's BBC interview, Mr Johnson said when he spoke to Mr Darroch by telephone the ambassador told him he had not seen the debate himself although somebody had told him about Mr Johnson's comments.
He added: "I think that unfortunately what I said on that TV debate was misrepresented to Kim".
That came as British police opened an investigation into the leak.
The Brexit Party's Diane James reflected on how could the scenario pan out regarding the fact that the House of Commons is likely to prevent whoever replaces Theresa May in Number Ten Downing Street from prorouging parliament to drag Brexit over the line and the European Union seems certain to stick to its guns.
"Boris is, I believe the necessary choice for our Prime Minister at this crucial time and moment in history", she said.
She said she had achieved an "enormous amount" in three years in the job.
"On the one hand, some people who'd always campaigned for Brexit, but didn't vote for the deal because they had a particular vision of Brexit and they were sticking firmly to that vision". But she was sorry about having to leave when "there was more that I wanted to do".
"On the other side, people who said they didn't want to leave with no deal, but weren't prepared to vote for a deal in order to make sure that what they wanted happened".
"This is complete news to the speaker - no such proposition has been put to him", she said.
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