Eurosceptic Conservative MPs have hit back at the trade secretary, Liam Fox, for “ludicrously tilting at windmills”, after he rejected Boris Johnson’s claim that exporters would be spared tariffs if Britain left the EU without a deal.

The former foreign secretary has promised to take Britain out of the EU on 31 October, with or without a deal, “do or die”.

And Johnson has suggested that in the event of a no-deal exit his government could seek to use article 24 of the general agreement on tariffs and trade (GATT) to secure a temporary standstill, while details of a new trade deal are hammered out.

Fox is an enthusiastic Brexiter, but supports Jeremy Hunt against Johnson.

He published a letter he had sent to a constituent on the jobs website LinkedIn on Tuesday, insisting it would not automatically be possible to have a tariff-free “standstill” in the event of a no-deal Brexit on 31 October.

“It has been claimed that in place of the implementation period we could immediately establish an interim agreement under this provision. However, in this scenario, the UK would still require the consent of the EU to the terms of that agreement, with an agreed plan and schedule for implementation,” Fox said.

“A ‘no deal’ scenario, by definition, suggests that there would be no mutual agreement between the UK and the EU on any temporary or permanent arrangement. In those circumstances Article XXIV cannot be used.”

He added: “The European Union has made it clear on a number of occasions that full tariffs will be applied to the United Kingdom in the event of ‘no-deal’.”

The risks of a no-deal Brexit are at the heart of the clash between the two men vying to become the next prime minister in just over four weeks’ time.

Johnson has been backed by many of the “Spartans” in the Tory party, including the European Research Group (ERG) deputy chair Steve Baker, who refused three times to vote for Theresa May’s withdrawal agreement, and want to see it junked.

But another vocal group of Conservative MPs, including Ken Clarke and Dominic Grieve, have warned they are ready to bring down a future Tory government rather than allow a no-deal Brexit.

Baker hit back against Fox on Wednesday, saying: “By stating the obvious, by repeating common ground as if there were any disagreement, Liam is ludicrously tilting at windmills. He’s done much to promote trade and freedom but I couldn’t be more disappointed in him here.”

He highlighted tweets by his ERG colleague Marcus Fysh, who claimed Johnson would “offer” the EU a temporary, tariff-free standstill period; and expected that offer to be taken up.

“As the draft withdrawal agreement will not pass, the EU will need to decide whether it wants to accept Boris’s offer of zero tariff trade to continue for the time being after Brexit on 31 October,” Fysh said.

The two sides would then notify the WTO of their intentions, under Gatt 24.

Gatt was the founding treaty of what became the World Trade Organization (WTO) – but trade experts say Gatt 24, as it is known, was only ever intended to operate where an outline trade deal has already been secured.

Johnson conceded that point himself in an LBC interview on Tuesday, saying “there has to be an agreement on both sides”, adding that the Bank of England governor, Mark Carney, was “wrong in thinking it’s not an option”.

Johnson has won the support of the ERG by taking a firm stance on Brexit; but has also convinced moderate Tories, including the health secretary, Matt Hancock, that he will govern from the political centre ground once Britain has left the EU.