The government and Labour have sought to blame each other after cross-party talks to find a compromise Brexit plan collapsed, leaving any remaining hopes of an imminent solution to the impasse in tatters.

While both sides insisted the discussions had taken place in good faith, Theresa May said a sticking point had been Labour splits over a second referendum.

Labour in turn said the government had been unwilling to compromise and that May’s imminent departure from Downing Street meant there was no guarantee any promises would be kept by a successor such as Boris Johnson.

Nick Boles, the former Conservative MP who helped spearhead efforts to prevent a no-deal Brexit in March, said he now feared such a departure was almost inevitable when the EU27’s latest deadline of 31 October is reached.

“It’s game over,” he said. “We only won by one, and it’s very unclear that we would have the same level of Tory support, and for that matter Labour support. We are absolutely convinced that parliament will not find a way to stop no-deal Brexit.”

The conclusion to six weeks of intermittent talks, which had angered many Conservative and Labour MPs who feared the nature of the compromise that might result, came with the release of a letter from Jeremy Corbyn to May on Friday.

Facebook Twitter Pinterest May at the launch of the Tory’s European election campaign in Bristol, with Conservative MEP candidates. Photograph: Toby Melville/PA

Despite praising the talks as constructive, the Labour leader wrote: “It has become clear that, while there are some areas where compromise has been possible, we have been unable to bridge important policy gaps between us.

“Even more crucially, the increasing weakness and instability of your government means there cannot be confidence in securing whatever might be agreed between us.”

May’s spokesman said the view was mutual: “It was clear to the government … that the talks were not going to reach a successful conclusion.”

Corbyn’s letter cited examples of what he said was May’s inability to carry her government on possible compromises, for example ministerial dissent over a possible customs union and the idea of allowing reduced food standards to secure a US trade deal.

Speaking in Bristol at a campaign event for next week’s European elections, the prime minister said the negotiations had “made progress”, but blamed Labour for the lack of an outcome.

Jeremy Corbyn (@jeremycorbyn) I have written to Theresa May to say that talks on finding a compromise agreement for leaving the European Union have gone as far as they can.



The government's growing weakness and instability means there cannot be confidence in its ability to deliver. pic.twitter.com/H27qxDleaB

“In particular, we haven’t been able to overcome the fact that there isn’t a common position in Labour about whether they want to deliver Brexit or have a second referendum and try to reverse it,” she said.

A Downing Street source said Sir Keir Starmer’s strong support for a second referendum was a particular sticking point. “It is clear that the shadow Brexit secretary has fairly strident views on the issue, and he led the Labour team in the negotiations,” the source said.

Starmer told the Guardian earlier this week that he believed it would be impossible for any deal to pass without a confirmatory referendum attached.

The Brexit secretary, Steve Barclay, echoed the point during a visit to Northern Ireland, saying the talks collapsed because of “division in the Labour party over the second referendum”.

In a sign of what is likely to be a fierce debate within government in the wake of the collapse, Barclay insisted it would be possible to “mitigate the disruption” of a no-deal Brexit.

Labour hit back at this narrative, with Starmer saying May was “trying to blame everyone but herself” for the collapse of the talks. He tweeted: “She knows the reality is she couldn’t carry her own side or offer a realistic compromise. Any deal agreed wouldn’t last a day under a new Tory leader.”

Facebook Twitter Pinterest Shadow Brexit secretary Keir Starmer, who led Labour’s negotiations, is a strong advocate of a second referendum. Photograph: Sean Smith/The Guardian

The tortuous process of discussion, which saw occasional meetings between May and Corbyn and many more involving their frontbench teams and officials, had been widely predicted to come to an end, but the news was still enough to see the pound drop to its lowest level against the dollar since February.

Corbyn had come under mounting pressure from within the shadow cabinet to walk away from the talks, including from close allies who feared a stitch-up that would see Labour blamed as the facilitator of a “Tory Brexit”.

Both sides stressed that some progress had been made, with the prime minister’s chief Brexit negotiator, Ollie Robbins, in Brussels earlier this week to discuss a joint draft of proposed changes to the political declaration about Britain’s future relationship with the EU27.

But while there were signs the two leaders were not miles apart, a number of Conservative MPs were agitated at the idea of a possible customs union, Corbyn’s key demand, while many in Labour disliked the prospect of a plan not being endorsed by a second referendum.

The government intends to press ahead with holding a vote on the withdrawal agreement bill in the week beginning 3 June – but sources stressed it would include “new features that reflect some of the discussions”, in the hope of winning over Labour MPs.

May also plans to resume talks with the Democratic Unionist party, with which she is in a confidence and supply partnership, about how it could be reassured that accepting the deal would not undermine the integrity of the UK.

Government sources also pointed to progress on considering “alternative arrangements” for the Northern Irish border – one of the central concerns of Brexiters who have held out against the deal.

Corbyn said Labour would “carefully consider” any new proposals, but added: “I should reiterate that, without significant changes, we will continue to oppose the government’s deal as we do not believe it safeguards jobs, living standards and manufacturing industry in Britain.”