Theresa May’s admission in Brussels that the UK could stay tied to the EU for a year longer has prompted an angry backlash from Conservative backbenchers, who said the prime minister was “desperate” and “reneging on everything”.

Her failure to deny reports that she had told the Irish she accepted the backstop to avoid a hard border could not be time limited prompted yet more concern, with Tory MPs warning it raised questions over whether the UK would really leave the EU.

The prominent Brexiter Priti Patel said an extension would not “in any way” solve ongoing concerns about the Irish border. “If the EU is refusing to help us to solve the border issue now, why will it take another three years to resolve it?” she wrote in a piece for the Guardian.

“I see no point in us building a bigger bridge to nowhere. Why would we extend the transition phase when we don’t know where or what we’re even transitioning to?”

Quick Guide Brexit and backstops: an explainer Show A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

The former minister John Penrose, an ex-remainer who is now amember of the hard Brexit European Research Group, said it was essential that the extension was not a “bridge to nowhere”.

He added: “There is a distinction between an implementation period and an extension to negotiations. If it is anything other than a period of time to implement something that has already been agreed, then people are going to question whether we will ever really leave. It kicks the can down the road and is the beginning of sliding into not delivering what people voted for.”

Even though No 10 appealed to Tory MPs to keep “cool, calm heads” over the proposal, the anger in Westminster spread beyond Brexiters. Anna Soubry, an outspoken remainer, said May was “reneging on everything” that had previously been agreed.

One former cabinet minister said they were dismayed at the impasse, warning that dissatisfaction with any carve-out for Northern Ireland extended well beyond the ERG. “Things are going badly wrong for Britain and things are not necessarily ‘just going to be OK’,” they said.

“We could end up in a terrible state and Tory MPs should be under no illusion that our party’s long-term fate is inextricably linked with this approach to Brexit and the prime minister’s mishandling of it.”

Nick Boles, a former Tory minister, described the attempt to extend the transition period as a “desperate last move”, suggesting May was losing the confidence of her party with many MPs “close to despair” over her plans.

“It’s a classic of negotiations that she keeps on thinking that one more concession is going to somehow [succeed], with one bound and she’s free, and she’s not going to be free, she’s getting ever more trapped,” he said.

Boles, a close ally of the Brexit-backing environment secretary, Michael Gove, has suggested an alternative arrangement that would see the UK enter a Norway-style European Economic Area arrangement with the EU, which would act as a bridge to an eventual trade deal.

Tory sources said Boles had met senior members of the ERG on Thursday to discuss his proposal, but that it was unlikely to win support. “It is so obvious this is a potential get-out route for Gove,” one MP said. “It is a pipe dream that we can leave with a soft Brexit and then toughen it up.”

Other MPs, including cabinet ministers, urged restraint, and among the majority of usually loyal Tory backbenchers there was still a sense that the prime minister should be given the benefit of the doubt until December.

“It’s any threat to the union that would be a real problem,” another centrist Tory MP said. “And I think most of us could take a brief extension to transition, but anything beyond, say, six months would be difficult.”

The justice secretary, David Gauke, told the Guardian: “There is a danger at this stage that you go through a bit of rollercoaster and every time it looks like you are making progress there is a degree of ecstasy, and every time there is no progress, people drop into the depths of despair. The answer is – this is going to be tough, there will be ups and downs.”

He criticised Tory colleagues who suggested tearing up what had already been agreed with the EU and starting again. It follows a letter from five ex-cabinet ministers, including Boris Johnson and David Davis, who urged May to reject both a Northern Ireland backstop and, crucially, an all-UK version.

“That sets us inevitably into no-deal territory and in those circumstances it’s very hard to predict … but some of my colleagues could potentially be putting Brexit at risk if they do that,” Gauke said.

“We need to honour the referendum result and do so in a way that protects jobs, the economy and the integrity of the United Kingdom. There are some complexities in that, it’s a challenging process and if we need to take a little bit of time to get that right, that seems to be a perfectly sensible thing to do.”