Tory and Labour MPs have united in their criticism of Theresa May following a defiant Downing Street speech in which the Prime Minister continued to argue the merits of her Chequers proposal for exiting the EU.

Despite being roundly rejected by EU leaders in Salzburg Mrs May stuck to the argument that Chequers was the best way to “protect jobs” and “avoid a hard border between Ireland and Northern Ireland”.

Former education secretary Justine Greening said the Prime Minister’s approach was now “neither fair, nor sensible”.

Appearing on BBC News she said: “I just think for any Government on an issue so important to our future as Brexit, a strategy of just guessing what the British public want and then hoping that it will work out okay from my perspective is simply neither fair nor sensible politically.

“That’s why I think it would be wise for her to start listening to MPs in her own party and indeed people in the country. The latest opinion poll showed just 14% of people supporting Chequers. That is not carrying out the will of the British people.”

Tory Brexiteer Jacob Rees-Mogg, who chairs the powerful European Research Group, praised Mrs May for being “strong and forthright” in her speech, but also urged her to ditch Chequers.

He said: “There is still no reason to suppose that Chequers can work either for the UK or the EU.

“It is time for the Government to start putting forward as its plan a Canada-style free trade agreement for the whole of the UK.

“This is the most realistic approach and similar to the EU’s proposal.”

Labour leader Jeremy Corbyn said that the Prime Minister had shown herself to be “incapable of delivering a good Brexit deal”.

He said: “Theresa May’s Brexit negotiating strategy has been a disaster. The Tories have spent more time arguing among themselves than negotiating with the EU.

“The political games from both the EU and our Government need to end because no deal is not an option.”

Shadow Brexit secretary Sir Keir Starmer accused the Prime Minister of being “in denial” over the Chequers proposals.

Sir Keir, speaking to BBC News, said: “The Prime Minister’s negotiating strategy is collapsing around her and that’s why we’re in this impasse and the country is staring down the barrel of no deal.

“I think the levels of anxiety are going up around the country day after day and the Prime Minister I think is appearing to be in denial.

“I don’t understand why she’s failed to hear the message that the Chequers proposal wasn’t going to be accepted by the EU and frankly it’s not going to be accepted by her own party.”