The Conservative Party could lose four million voters if it takes a harder line on Brexit and tries to “outdo” Nigel Farage, the newest Cabinet minister has warned.

Rory Stewart, MP for Penrith and the Border who was appointed International Development Secretary last week, said Remain supporters would abandon the Tories if they made such a “mistake”.

“Most Brexit voters voted for the Conservative Party but four million Remain voters voted for the Conservative Party,” he told Sky News’ Sophy Ridge On Sunday.

“If the Conservative Party were to make the mistake of trying to outdo Nigel Farage, which I’m sure we won’t but it is something that a few of my colleagues are talking about, then we would lose those four million voters.

“We’d lose young people, we’d lose Scotland, we’d lose London and we’d lose a lot of the most energetic parts of this country.

“We’ve got to be a broad party. We’ve got to be able to stretch all the way from Ken Clarke right the way through to Jacob Rees-Mogg.”

His warning came as a spat emerged between the Government and Labour Party over newspaper reports outlining where the PM is preparing to give ground this week in the negotiations.

Shadow chancellor John McDonnell accused Theresa May of jeopardising the cross-party negotiations for her own “personal protection”, saying he had lost trust in her and claimed the PM had “blown the confidentiality” of the talks.

Discussions between Labour and the Government are expected to continue tomorrow. Last night, Mrs May urged Jeremy Corbyn to work with her party to find a way to break the Brexit deadlock.

She wrote in Mail on Sunday: “To the leader of the opposition, I say this: let’s listen to what the voters said in the elections and put our differences aside for a moment. Let’s do a deal.”

Mr Stewart told Sky: “I think a deal can be done, a lot of this rests on... whether Jeremy Corbyn really wants to deliver a Brexit deal.

“But I think if he wants to do it, it will be actually surprisingly easy to do because our positions are very, very close.”

He also confirmed that he would run to be the next prime minister when Mrs May stands down, but said: “I am now so excited to be the International Development Secretary.”

Elsewhere, Brexit Party leader Mr Farage challenged Mr Corbyn to a debate ahead of the European elections, warning a deal between Labour and the Tories would be the “final betrayal”.

He told Sky: “There are five million voters out there, Labour voters, who voted to leave, particularly in the Midlands, the north, and south Wales.

“I would love between now and polling to have a debate with Jeremy Corbyn about this because people are very confused about what Labour are standing for.”

Shadow health secretary Jon Ashworth said the Government was trying to re-dress their customs union offer and has not really shifted its position.

“The key thing is the Government want to be able to do their own trade deals and my concern is that if we have a trade deal with the United States, for example, that could mean Trump’s America and big private healthcare corporations getting their hands on NHS contracts.”