Philip Hammond, the chancellor, has said it is “terrifying” that one of Boris Johnson’s close allies, Jacob Rees-Mogg, believes a no-deal Brexit will boost the economy.

The chancellor, who is expected to exit the government next week, expressed his horror after Rees-Mogg used a Daily Telegraph opinion piece to dismiss the “pure silliness” of Treasury forecasts suggesting a £90bn hit to the economy.

Rees-Mogg claimed there were economic models that showed “the total positive impact of no deal could be in the region of about £80bn”.

Hammond hit back at the argument, saying on Twitter: “Happy to debate scale of negative impact of no deal on the economy – but terrifying that someone this close to a potential future government can think we’d actually be better off by adding barriers to access to our largest market.”

Rees-Mogg told the Guardian this was part of “project fear”, which he claimed had been “consistently wrong”, adding that his article made clear that the “barriers to trade that the chancellor is fretting about would be against World Trade Organization rules, while he ignores the benefits of future trade deals”.

The clash highlights the looming problems that Johnson is likely to have as prime minister if he wins the Tory leadership contest next week.

He has said he wants a deal with the EU that scraps the Northern Ireland backstop by the end of October, but if that fails, many of his Eurosceptic backers are keen to proceed to a no-deal Brexit.

Hammond is one of many senior Tories on the other wing of the party who will fight hard against that outcome, with the chancellor even suggesting he could vote down his own government to stop it.

Johnson has not ruled out proroguing parliament to achieve a no-deal exit but Andrea Leadsom, one of his backers, suggested she was among those who would not support that and did not believe he would go for it.

Q&A What does 'prorogue parliament' mean? Show Hide Prorogation is the official term that marks the end of a parliamentary session. After being advised to do so by the prime minister, the Queen formally prorogues parliament. This takes the form of an announcement in the House of Lords on the Queen’s behalf. It is a speech, written by the government, which usually describes the bills that have been passed during that session and summarises what has been achieved. It means that all work on existing legislation stops, and MPs and Lords stop sitting. Prorogation also automatically kills any bills, early day motions or questions to ministers going through parliament. Parliament can then be reopened a few days later with a fresh slate of legislation intentions, set out in a new Queen’s speech at the formal state opening of parliament.

Stephen Barclay, the Brexit secretary and a supporter of Johnson, told a Commons committee on Wednesday that no-deal Brexit was “underpriced” and he believes preparations needed to be ramped up.

Following reports that he clashed last week with Michel Barnier, the EU’s chief Brexit negotiator, by telling him the EU withdrawal agreement was dead, Barclay said this was “not a controversial observation”.

“In terms of the withdrawal agreement, what I said was that the House had rejected it three times, including the third time by a significant margin; that the European election results in my view had further hardened attitudes across the house and that the text, unchanged, I did not envisage going through the house,” he said.

He said: “A no-deal Brexit would be disruptive,” but added: “No Brexit is the worst of those two outcomes.”

Barclay also revealed that the government was looking at compensating sheep farmers in the event of a no-deal Brexit, following warnings from the National Farmers’ Union that this would result in shepherds being forced to slaughter their flocks because there would be no market for their meat.

He said the sheep meat industry was an “outlier” because 97% of exports went to the EU but the government was working on intervention measures and compensation.

Barclay set out his view that parliament would be asked to vote on any new deal achieved by the next prime minister, and then if that was rejected, it would be offered a choice of revoking Brexit or leaving with no deal.

“But the question then will be is there a deal that is palatable to parliament and if not will parliament vote to revoke or will we leave with no deal?”

However, any prime minister going down that path could face a no-confidence motion first. Tory backbenchers fighting a hard Brexit, including Hammond, Dominic Grieve, Justine Greening and Guto Bebb, would have to weigh up whether to vote to bring down their own government and risk a general election rather than allow the UK to depart on no-deal terms.