Jacob Rees-Mogg has criticised Theresa May over her handling of Brexit negotiations, calling the prime minister’s stance on the Irish border “an error” and “a mistake”.

The arch Brexiteer said Ms May was wrong to refuse to play hardball with Brussels by daring it to set up a hard border in Northern Ireland if there is no Brexit withdrawal agreement.

He also criticised the cabinet’s decision to approve a “backstop” option that would see Northern Ireland fall under the same regulations as the rest of Europe for a time-limited period if no other deal is reached, describing it as a “real problem”.

Mr Rees-Mogg has previously urged Ms May to “call their bluff” during negotiations and argue there will only be a hard border after Brexit if the EU creates one, thereby giving Brussels sole responsibility for finding a solution to the problem.

He said: “Ireland has said it doesn’t want a hard border, the UK has said it doesn’t want a hard border and the EU itself has said it doesn’t want a hard border – so frankly it’s up to Brussels if it wants to start putting up border posts. We should call their bluff.”

He was reportedly rebuked by Ms May for the suggestion.

The North East Somerset MP told the BBC’s Andrew Marr Show the prime minister’s refusal to adopt his proposed approach was “an error”.

He said: “The prime minister said in her Mansion House speech that she wasn’t going to do this. I think that is a mistake. I think it is the obvious negotiating position for us to have.

“Bearing in mind the Irish economy is heavily dependent on its trade with the United Kingdom, it is overwhelmingly in the interests of the Republic of Ireland to maintain an open border with the United Kingdom.

“I think if you’re going into a negotiation you should use your strongest cards, and just to tear one of them up and set hares running on other issues is, I think, an error.”

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Mr Rees-Mogg also criticised the cabinet’s decision to agree a “backstop” option that would see Northern Ireland maintain the same regulatory system as the rest of the EU customs union for a “time-limited” period if no deal is reached to avoid a hard border.

He said: “That’s a real problem because the customs union on its own does not solve the seamless border issues ... you require regulatory alignment as well, and that means the single market.

“If we were to stay as a rule-taker, as a vassal state, for an indeterminate period, I don’t think that would be delivering on Brexit. And if you offer a backstop that is more attractive than anything you’re likely to negotiate, from the other side’s point of view, the backstop ends up becoming a frontstop.”

He added: “There are concerns, inevitably, at the way negotiations are proceeding.”

Irish Deputy Prime Minister Simon Coveney says a hard border with Northern Ireland won't work

However, the MP, who chairs the European Research Group of anti-EU Tory MPs, dismissed suggestions he could launch a leadership challenge against Ms May if she fails to deliver the hard Brexit that Eurosceptics are demanding.

He said: “I think the prime minister is the most impressive and dutiful leader that this country has had.

“Her expression of duty is something that Conservatives should admire and applaud.”

He added: “Of course I wouldn’t challenge Theresa May – that’s a ridiculous idea. The prime minister has my full support to remain as leader of the party, as I’ve said many times.

“I don’t wish to be prime minister. I’m very happy to be a backbench member of parliament.”

And in a sign of Brexiteers’ concern that a new Conservative leader could be less favourable to their vision of Brexit, he added: “I think Mrs May is crucial to the Brexit project.”

Mr Rees-Mogg also revealed he had been told the EU Withdrawal Bill would return to the House of Commons in mid-June. Ministers have refused to confirm when the flagship bill will next be voted on by MPs, with the delay widely seen as a result of attempts to ensure the government has the numbers to overturn the 15 amendments made by the House of Lords.

It comes amid reports Mr Rees-Mogg has purchased a new £5m house just yards from Parliament, fuelling speculation about his leadership ambitions. The property, on Cowley Street in Westminster, was previously the headquarters of former Tory chairman Lord Ashcroft.