Jean-Claude Juncker has called on the British government to publish its Brexit plan in full after Boris Johnson was accused by Ireland’s prime minister of misleading parliament over the impact on the Irish border.

The move came on a dramatic day during which Johnson’s hopes of securing a deal by the time of a crunch summit appeared to unravel:

The European parliament’s Brexit steering group insisted the UK proposals did not “even remotely” amount to an acceptable deal for the EU.

Donald Tusk, the European council president, said Brussels was “unconvinced” by Johnson’s plans, and offered the EU’s full solidarity with Ireland amid claims that Dublin was under pressure to compromise.

The EU agreed to set David Frost, the prime minister’s chief negotiator, a deadline of one week to offer fresh solutions on the key sticking points.

Arlene Foster, leader of the Democratic Unionist party, which has given its backing to Johnson’s plans, insisted that the Irish taoiseach, Leo Varadkar, would “go down in history as the man that instituted a hard border on the island of Ireland” if he failed to swallow the UK’s proposals.

Johnson’s plans for a whistle-stop tour of EU capitals was put in peril after failing to fix meetings with both the German chancellor, Angela Merkel, and Emmanuel Macron, the president of France, due to “scheduling problems”.

Juncker’s call came after the European commission president spoke on the phone to Varadkar. He then issued a statement saying the two men agreed that the UK should open the legal text tabled on Wednesday to public scrutiny.

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The UK has so far only made public a seven-page explanatory document on its proposals. The government has insisted that the full 44-page legal text given to the European commission be kept confidential.

“Both the president and the taoiseach agreed that they would be in favour of the UK publishing the legal text of their proposal,” a statement from the commission said.

A senior EU diplomat said: “We want transparency and openness now – let’s stop playing hide and seek.”

A UK source said: “It is perfectly normal for proposed legal texts to remain confidential during detailed negotiations.”

Play Video Boris Johnson says his Brexit deal shows 'great flexibility' – video

The extraordinary intervention by the two leaders reveals the plummeting level of trust with Downing Street amid fears the prime minister is merely seeking to blame Brussels for a failure to find a deal.

Earlier in the day, Varadkar had queried Johnson’s response in the Commons to a question from the former cabinet minister Damian Green, a close ally of Theresa May.

The prime minister had insisted that a customs border on the island of Ireland would “absolutely not” require new infrastructure for checks and controls.

“I am reassured by what Prime Minister Johnson said today: that he is not proposing that there should be any new physical infrastructure on the island of Ireland linked to customs or customs checks – but that is actually in contradiction to the papers presented by the UK government yesterday,” Varadkar told reporters. “I don’t fully understand how we can have Northern Ireland and the Republic of Ireland in a separate customs unions and somehow avoid there being tariffs and checks and customs posts between north and south.”

Quick guide Why is the Irish border a stumbling block for Brexit? Show Hide 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

In a further barbed comment, Varadkar suggested the British public had changed its mind on Brexit but was being prevented from having its voice heard. “All the polls since Mr Johnson became prime minister suggest that’s what the British people actually want, but their political system is not able to give them that choice,” he said.

The government has proposed that the whole of the UK leaves the EU’s customs territory but that Northern Ireland stays in the EU’s single market for goods if the Northern Ireland assembly at Stormont agrees in a vote before the end of the transition period, and then every four years.

During a briefing of member state’s ambassadors on Thursday evening, the EU’s chief negotiator, Michel Barnier, gave a damning critique of the proposals, telling the diplomats that it was difficult to see a deal emerging in the next 10 days unless the British “fundamentally amend their position”, according to EU sources.

Brussels has consistently stressed the agreement must be complete before leaders attend a crunch EU summit on 17 October. “You can’t just get to the European council and just say ‘here is the text, take it or leave it,’” an official said.

At the meeting, Barnier was withering about Johnson’s characterisation of the border as a question of technicalities. The EU negotiator stressed that peace in Ireland and the all-Ireland economy were at stake.

Facebook Twitter Pinterest Michel Barnier speaks to the media outside the EU headquarters in Brussels on Thursday. Photograph: Virginia Mayo/AP

The Frenchman was tasked by EU member states to find out what room for manoeuvre the British have, as the EU continues to assess whether a deal is possible. Finding out if there is space for a deal will be one of the top points of the agenda for talks on Friday with Frost.

One EU diplomat said any decision to intensify talks hinged on compromise from the UK: “What the EU will test is their flexibility. Are they willing to move more on the customs issue?” the diplomat said, raising one of the EU’s major problems with the proposals. “This has to happen extremely quickly since time is in extremely short supply.”

No ambassador wanted to reject the British proposals outright, but they are seeking to understand whether the British will move further, not only on customs, but also on the proposed “Stormont lock”, a deeply problematic idea for the EU because it puts the status of Northern Ireland up in the air every four years, and appears to give the DUP a veto.

Despite supportive words from Tory backbenchers, the EU remains far from convinced Johnson can get the deal through the Commons. “There is a doubt here,” the diplomat said. “Boris Johnson has lost every vote in parliament. And we remember Theresa May has said there would be a majority. So maybe it’s history repeating itself.”

