Conservative cabinet minister insists Theresa May’s Brexit deal is alive despite all 27 EU leaders saying it's dead

A Tory cabinet minister has insisted Theresa May’s Brexit deal is “still credible”, despite a humiliating rebuff from all 27 European Union leaders.

The prime minister was left fighting to save her Brexit blueprint and her leadership after a key summit in Salzburg on Thursday, where EU chief Donald Tusk said a crucial part of her plan "will not work".

James Brokenshire, the housing secretary, dismissed the rejection as "tough words" as part of the EU's negotiating strategy and said the government was still "resolute" in seeking a deal.

But behind the scenes, senior Tories including home secretary Sajid Javid, Commons leader Andrea Leadsom and Esther McVey, the work and pensions secretary, are considering pushing the government away towards a Canada-style deal, The Times reports.

It comes ahead of a turbulent Conservative party conference, where Ms May is likely to face pressure from on all sides over her Brexit strategy.

Mr Brokenshire told BBC Radio 4's Today programme: “The prime minister is acting in the national interest, she’s sticking up for Britain, and the Chequers deal is a workable, credible deal to meet our ambitions, our intent.

"Should we be surprised that there are tough negotiations, tough words? No, because we are entering the final phase of those negotiations to get the deal and we remain resolute in getting that and getting that deal for our country.”

Mr Brokenshire insisted that Ms May's plan was still the only viable option as the EU's preferred option would risk breaking up the United Kingdom by creating a hard border in Ireland.

"The easy thing for the prime minister to do would be to go with one of those two options that are being proffered," he said.

"EEA, which does not deliver on what the people voted for in the EU referendum on freedom of movement, or Canada, which would effectively break up the UK.

"The Chequers deal is a workable, credible deal to meet our ambitions.

"They have said that it's about the integrity of the single market and we believe the Chequers deal responds to that, and it's for the EU to engage with what's on the table, which is actually Chequers Two."

The government is "preparing hard" for a no-deal Brexit if the impasse over Northern Ireland cannot be broken, said fellow cabinet minister Chris Grayling.

The transport secretary told Newsnight: "We're not going to accept a border between Northern Ireland and the rest of the United Kingdom.

"We are now preparing hard for the option of a no-deal Brexit. We don't want to get there, we don't expect to get there.

"But our European partners if they want to reach a deal, have to find a way of understanding that there are some things we cannot accept."

The so-called Chequers deal has drawn criticism from Eurosceptics and pro-EU alike since it was unveiled by the prime minister in July, prompting the resignations of both Boris Johnson and David Davis in protest.

Brexiteers dislike Chequers due to the proposals for a common rulebook, which they believe will keep the UK too closely aligned to the EU, while European leaders reject any plans that could compromise the integrity of the single market.

Former Tory leader Iain Duncan Smith questioned why the prime minister's Chequers plan had been pursued in the first place, when it was clear the EU could not accept it.

He said: "This advice has been off from the word go.

"From the word go there have been question marks over why we were pursuing this when it's quite clear and obvious the EU couldn't accept it.

"Him [Olly Robbins - Ms May's chief Brexit adviser] and others, the whole team, really need to look at this - why we were on Chequers when Chequers so obviously wasn't going to cut the mustard."

The next Brexit milestone is fast approaching, with the October 18 summit labelled a "moment of truth" by Mr Tusk.

An additional Brexit summit could be held in November, but only if a deal is within reach.