The Brexit secretary, Stephen Barclay, has said the EU is facing a “moment of truth” next week after his latest round of talks with Michel Barnier ended with both sides seeking to shift the blame for the impasse.

The UK government is expected by EU officials to table formal proposals next Thursday after the Conservative party conference, but talks on Friday wound up in apparent acrimony.

With the two sides sharply divided, both the EU and the UK sought to lay responsibility for the lack of agreement on the other, in a sign of the futility of the recent negotiations.

The European commission president, Jean-Claude Juncker, said the ignominy for a lack of a deal would lie with the UK. “If this fails in the end, the responsibility lies solely with the British side,” he said.

Barclay told reporters there “needs to be political will on both sides and we’re now approaching the moment of truth in these negotiations”.

He added: “We are committed to securing a deal, the prime minister has made clear he wants a deal but there has to be political will on both sides and that’s what we’re exploring.”

Barclay and Barnier clashed in correspondence over no-deal contingency measures with the British cabinet minister seeking greater cooperation. Barnier insisted that he would not accept “mini deals” and that the withdrawal agreement was the only vehicle for dealing with the outstanding issues.

It is understood that the French government is insisting that serious proposals must be seen within a week, complaining that they do not want Brexit to overshadow other issues when EU leaders meet at a summit on 17 October.

Berlin has privately described the papers so far put forward as “completely insufficient”, according to a leaked diplomatic note of a recent meeting of ambassadors in Brussels, seen by the Guardian.

It is understood formal papers will be presented next by the UK but there is growing and grave scepticism in Brussels that the British government will be able to produce anything reasonable for EU leaders to sign off on 17 October.

The UK has insisted Northern Ireland cannot be “left behind” in the EU’s single market and shared customs territory, nor can the whole of the UK be “trapped” in the bloc’s structures simply to avoid a hard border.

Barclay emphasised in a recent speech in Madrid that any deal must recognise there will be two regulatory zones on the island of Ireland. The government says controls and checks on trade through the border can be done in a light-touch way to ensure there is no infrastructure or huge changes to the local economy.

The EU has said that, as yet, there does not appear to be any solution beyond Northern Ireland and the Republic of Ireland remaining in regulatory alignment. “What they are proposing is for us to ignore huge blocks of EU law – make massive derogations for them,” a source said. “It doesn’t work.”

On the eve of his meeting with Barclay, Barnier had told EU ambassadors that the proposals so far tabled by the UK were not workable. He reiterated that time was running out, adding in an aside that the dramatic scenes in Westminster did not offer much confidence that a majority for any deal could be found.

Quick Guide Why is the Irish border a stumbling block for Brexit? Show Counties and customs Inside the EU, both Ireland and Northern Ireland are part of the single market and customs union so share the same regulations and standards, allowing a soft or invisible border between the two.

Britain’s exit from the EU – taking Northern Ireland with it – risks a return to a hard or policed border. The only way to avoid this post-Brexit is for regulations on both sides to remain more or less the same in key areas including food, animal welfare, medicines and product safety. The 'backstop' in Theresa May's Withdrawal Agreement was intended to address this - stating that if no future trade agreement could be reached between the EU and the UK, then rules and regulations would stay as they are. This has been rejected by Brexit supporters as a 'trap' to keep the UK in the EU's customs union, which would prevent the UK striking its own independent trade deals. There are an estimated 72m road vehicle crossings a year between Northern Ireland and the Republic of Ireland, and about 14% of those crossings are consignments of goods, some of which may cross the border several times before they reach a consumer. Brexit supporters say this can be managed by doing checks on goods away from the border, but critics say it will be difficult to police this without any physical infrastructure like border posts or cameras, which could raise tensions in the divided communities of Ireland.

Interactive: A typical hour in the life of the Irish border Photograph: Design Pics Inc/Design Pics RF

“But the biggest obstacle to a deal remains the absence until now of serious, workable proposals,” a source said.

Several EU diplomats told Barnier the UK would have to table “serious” plans to replace the Irish backstop by the end of next week – immediately after the Conservative party conference in Manchester. “The clock is ticking, after that, time would be in too short supply,” an EU diplomat said.

But the person added that the mood around the table was highly sceptical that it would be possible to agree a deal, also because of the political situation in London.

If the UK fails to produce proposals within the next seven days, EU diplomats say their governments will not have enough time to assess the politically sensitive and deeply technical issues at stake.

The pessimistic mood deepened after the UK presented earlier this week its latest discussion paper on breaking the backstop deadlock – a six-page document on moving food, animal and plant products between Great Britain and Northern Ireland, as part of a plan for an all-Ireland agri-food zone.

EU diplomats are unhappy that the UK seems to be picking holes in the logic of the EU’s strict rules on food, animal and plant safety (sanitary and phytosanitary measures). “If you are staying in our SPS zone you don’t get to start second guessing the logic of it,” said one source, describing the mood. “I sense an extra frustration. There is a bit of a ‘how dare you’ kind of line.”

Voicing his frustrations, Barnier told the diplomats the UK was “basically asking us to organise shortfalls and imperfections at our border”.

While EU diplomats were focused on technical talks, many have been aghast at the UK prime minister’s performance in the Commons on Wednesday night.

“There was very little talk of recent developments in Westminster, if only to note that it seemed increasingly difficult to see how the government would obtain a majority for a deal, given the divisions getting more entrenched by the day,” a second diplomat added.

Speaking to reporters in Brussels, where he was seeing Barnier, Ireland’s deputy prime minister Simon Coveney said the UK had yet to put forward a “serious” proposal, with just four weeks to go before the country is due to leave.