The UK appears set to crash out of the EU without a Brexit deal due to the “intransigence” of the Brussels machine, Liam Fox has claimed.

The international trade secretary put the chances of a no-deal Brexit at “60-40” despite both sides saying they wanted to reach an agreement on the terms of the UK’s departure from the bloc in March 2019.

The prominent Brexiter said he believed the risk of a no-deal scenario had increased, pinning the blame on the European commission and Brussels’ chief negotiator, Michel Barnier.

“I think the intransigence of the commission is pushing us towards no deal,” he told the Sunday Times (paywall). “We have set out the basis in which a deal can happen but if the EU decides that the theological obsession of the unelected is to take priority over the economic wellbeing of the people of Europe then it’s a bureaucrats’ Brexit, not a people’s Brexit – then there is only going to be one outcome.”

He said Barnier had dismissed the UK’s proposals in the Chequers plan thrashed out by Theresa May and the cabinet because “we have never done it before”.

The government has admitted its proposals are unprecedented, but Fox said Barnier’s response “makes the chance of no deal greater”.

The prime minister held talks with the French president, Emmanuel Macron, on Friday, cutting short her holiday to visit his summer retreat.

Cabinet ministers including the foreign secretary, Jeremy Hunt, and the Brexit secretary, Dominic Raab, have also engaged in diplomatic activity in Europe in recent days as the government seeks to deal directly with individual governments in an effort to keep the Chequers plan alive.

In a sign that member states are being warned of the consequences of the failure to find a deal, Fox said: “It’s up to the EU27 to determine whether they want the EU commission’s ideological purity to be maintained at the expense of their real economies.”

Meanwhile, the former cabinet minister Priti Patel said May must ditch the Chequers plan, which would result in the introduction of a “common rule book” for goods with the EU, in effect tying the UK to terms set by Brussels.

Writing in the Telegraph, she said it did not meet the result of the referendum and would “leave us half-in and half-out, still bound to EU regulations and constraints”.

Calling for a looser free trade deal with the EU she said the change would take “political courage, the kind of courage that appears to have been lacking over the past two years”.

The Labour former cabinet minister David Blunkett used a Sunday Telegraph article to reject claims that people who voted to leave over immigration concerns were “racist” and said the result would be the same if there was another referendum.

He said people believed the political system did not reflect their concerns following the impact of the financial crash and austerity, in many places hitting communities struggling to cope with the aftermath of deindustrialisation.

“To understand this, and why, if there were to be a second referendum now, I believe that the majority would still vote to leave, is critical if we are to get our democratic system back on track,” he said.