Conservative Party candidates Jeremy Hunt and Tom Tugendhat have vowed to press ahead with Boris Johnson’s controversial legislation to unilaterally ditch Brexit checks in defiance of the EU.

The Remain-backing moderates have both promised to press ahead with the Northern Ireland Protocol bill, despite warnings it will break international law.

Mr Hunt suggested to regretted backing the Remain campaign – saying he would be “very tempted” to vote Leave – and vowed to make Brexiteer Esther McVey the job of deputy prime minister if he wins the contest.

Mr Tugendhat described Brexit as a “revolution” which could not be overturned. “There is no way back into the European Union. I would never vote to go back into the European Union. That’s over,”

The Remain campaigner also said the protocol bill was a good “negotiating leverage” to push the EU further on easing checks. “You have to keep the bill. You need to have the negotiating leverage,” he told the Sunday Times.

Mr Tugendhat also claimed he could both “reset” relations with Brussels and end the barriers between Northern Ireland and Great Britain. “There are two things that are going to change that dynamic. The first is the bill. The second is a change of leader.”

The foreign affairs select committe chair added: “I can deliver what we are asking for, Northern Ireland fully and completely part of the UK single market, without the risk to the Europeans that they currently claim.”

Mr Hunt told the Sunday Telegraph he would push the protocol bill through parliament if he wins, despite the EU’s warning the plan to rip up the Brexit withdrawal agreement would break international law and could spark trade retaliation.

The former minister, making his second bid at the leadership, also said “Brexit freedoms” must be embraced in an effort to make Britain a “powerhouse” economy.

Asked if he would now he vote to leave the EU if he could go back to the 2016 referendum, he said: “I would be very tempted to.”

Asked onn BBC Sunday Morning if he “blows with the wind” on Brexit, Mr Hunt said: “I have never doubted for one moment that we can make a hug success of being outside the European Union.”

Brexit opportunities minister Jacob Rees-Mogg said it was “very important” that the next leader could deliver on Brexit and press on with the protocol bill. “It’s needs to be someone who will support that.”

Sajid Javid, who entered the race on Saturday, said the UK should consider ripping up old EU laws “to make us a more pro-business, wealth-creating, entrepreneurial economy”.

The candidates have distance themselves from senior Conservative MP Tobias Ellwood’s call for a return to the EU single market to help ease the cost of living crisis.

Mr Tugendhat said the naughtiest thing he had ever done is “invade a country” – referring to his time in the military during the invasion of Iraq.

Meanwhile, Tory leadership campaign teams are reportedly drawing up dossiers full of compromising allegations against rival candidates and their aides.

At least two rival campaign teams are claimed to have handed Labour digital dossiers packed with allegations against potential opponents, according to the Sunday Times – with even candidates’ staffers supposedly targeted.

Labour MP Chris Bryant tweeted: “The stories circulating about the various leadership candidates are so lurid they’re difficult to credit, but even more bizarre is the fact Tory MPs are circulating them.”