Boris Johnson accused the Treasury of being ‘the heart of remain’. Photo: Will Oliver/EPA

In the private speech to the Conservative Way Forward group, Johnson is heard dismissing the cautious approach of Philip Hammond’s Treasury, which he said had focused on “mumbo jumbo” predictions about short-term disruption, instead of the potential gains from leaving the EU. He also portrayed Treasury as “the heart of remain.”

Theresa May still has full confidence in Johnson, a Downing Street spokeswoman said on Friday. But she refused to comment further on the leaked recording.

Labour and the Scottish National party have both called on May to sack Johnson over the remarks.

Earlier on Friday, the former Conservative leader Michael Howard, who, like Johnson, is a leading Brexiter but not one of his allies after firing him from his shadow cabinet, said the foreign secretary was right to criticise the Treasury.

“That fear of short-term disruption has become so huge in people’s minds that it’s turning them all wet,” he said. “Project Fear is really working on them.”

Speaking to BBC Radio 4’s Today programme, Howard said: “If there are people in the Treasury who are doing that, then they shouldn’t be, and I deplore that.”

He also played down the divisions in the cabinet that the secret recording exposed as the “spills and thrills” of the Brexit negotiations.

Howard claimed Johnson was joking when he spoke approvingly of a imaginary scenario in which Donald Trump was leading the Brexit talks.

Johnson was recorded saying: “He’d go in bloody hard … There’d be all sorts of breakdowns, all sorts of chaos. Everyone would think he’d gone mad. But actually you might get somewhere. It’s a very, very good thought.”

Johnson said he had become “increasingly admiring of Donald Trump” and has become “convinced that there is method in his madness”.

Asked about the Trump comments, Howard said: “That is a thought I would prefer not to entertain. I suspect he had his tongue in his cheek when he said it.”

In his speech, Johnson urged Tory donors not to panic during a likely “meltdown” over Brexit. Howard said: “He is certainly right to say we shouldn’t panic. I don’t know about a meltdown I’m not as close to the negotiations as Boris is. But there always going to be thrills and spills and what we have to do is to focus on the essentials of the situation.”

The Tory grandee attacked remainers on the Conservative backbenches for trying to “nudge” the prime minister into staying in the customs union.