Jacob Rees-Mogg has said Britain is heading for a no-deal exit from the EU, and that leaving on World Trade Organisation (WTO) terms is now likely.

Presenting a phone-in on LBC, the prominent Tory MP and hardline Brexiter said: “I think we are heading to WTO and I think WTO is nothing to be frightened of.

“I think we should carry on negotiating until the end. I don’t think we necessarily need the theatrics of walking away, but the truth is that WTO is likely to be all that they will offer us.”

He made his comments as Theresa May dug in on her Brexit offer to Brussels after the EU publicly doubted the controversial proposals were workable.

Government sources said the prime minister was “standing over” the Chequers cabinet compromise on withdrawal plans, despite the EU’s chief negotiator, Michel Barnier, mauling the initiative.

Barnier openly questioned the credibility of the UK’s proposals in his first response to the government’s Brexit white paper. He expressed concern that May’s suggestion of a “facilitated customs arrangement” opened up the risk of major fraud, additional bureaucracy and damage to EU businesses.

In comments that are likely alarm hard Brexiters in Tory ranks, the vice-president of the European parliament and MEP for Ireland’s governing Fine Gael party, Mairead McGuinness, made it clear that May would have to abandon some of her red lines to clinch a deal.

Speaking to the BBC, she said of London’s proposals: “It’s a starting point, it’s not an end deal. I think the British prime minister set out red lines too early on and too deeply.

“We are prepared to show flexibility if the British prime minister can show flexibility.”

The defence minister Tobias Ellwood insisted the white paper was a workable compromise. He told the BBC: “There is no yes/yes solution here which will balance out the extreme views of the Brexiteers and the extreme views of the remainers. It is therefore essential that we have compromise.

“And this is exactly what the white paper does. It means that we have for the remainers, we have access to goods and services, a deal with Europe as well. We have financial markets as well.

“And on the leave campaign side of things, the bill, the EU bill stops. We leave the customs union, we leave the agricultural policy, we leave the common fisheries policy, and, of course, we are able to strike our own deals.”

The leader of the House of Commons, Andrea Leadsom, said she hated the Chequers compromise, according to The Times, quoting minutes of the cabinet meeting at the PM’s country residence earlier in July.