THERESA May’s Justice Secretary has hinted that he could quit the Government if the Prime Minister allows a hard Brexit with the EU.

Speaking to the BBC, David Gauke said he would find it “very difficult” to remain in Cabinet if the UK was on course to crash out of Europe without a deal.

His comments came as the Government stepped up preparations for London and Brussels failing to agree a future trade deal.

Although there is no majority for a hard Brexit in Parliament, if there is no agreement reached by March 29, or no extension of the negotiating period, then the UK will crash out of the EU.

The Cabinet agreed on Tuesday that a no-deal Brexit should now be the “operational priority”.

Earlier this week civil servants removed claims that a hard Brexit is “unlikely” from dozens of official notices.

Gauke told the BBC’s Political Thinking podcast: “Making a conscious decision to proceed with no deal would not be the responsible course of action.”

He said he would be “very surprised if the Prime Minister went down that route”.

Asked if he could remain in the Cabinet if that became the Government’s policy, he said: “I think it would be very difficult for me in those circumstances.

“I am conscious that there is a risk of an accidental no deal … Although Parliament clearly doesn’t want no deal, it’s not clear that there is a majority for a specific course of action to stop no deal.

“The best way of stopping no deal is to back the Prime Minister’s deal in my view. So I think it would be very difficult and I think if it came down to the Government saying consciously, ‘well, we’ll just have to do that’, I don’t think there would be a lot of support for it.”

At a press conference on Thursday, May insisted the Cabinet was focused on the deal. “Everybody is very clear that not only what Government policy is but what we are all individually and collectively focused on is working to ensure that that deal is able to be agreed by and go through a meaningful vote in the House of Commons.”

The Prime Minister, facing certain defeat, delayed this month’s meaningful vote on her deal until January, ostensibly giving her time to ask Brussels for further assurances on the Irish backstop.

But those assurances have not been forthcoming and with no change in the deal, May will still likely overwhelmingly lose the vote when it goes in front of MPs.

There are tensions in Cabinet over what should happen now.

Earlier this week Amber Rudd said she could see “a plausible argument” for a second referendum, the so-called People’s Vote.

Her colleague, Andrea Leadsom, the leader of the House of Commons, disagreed, saying the legislation for the vote “would take months and months, if not well over a year”.

“I don’t understand why anybody thinks it is either a good idea or a practical idea,” she said.

Leadsom suggested the option of a managed no-deal Brexit.

“A managed no-deal does not necessarily mean there is no Withdrawal Agreement at all,” she told BBC Radio 4’s Today programme.

“This is all speculation, but what I am looking at is trying to find an alternative that, in the event we cannot agree to this deal, that there could be a further deal that looks at a more minimalist approach that allows us to leave with some kind of deal, and some kind of implementation period that avoids a cliff edge, that avoids uncertainty for businesses and travellers and so on.”