Theresa May has hinted that the UK could extend the Brexit transition period to allow more time for trade talks, but she dismayed leaders at a crunch Brussels summit by failing to offer any new ideas to break the impasse over the Irish border.

In a development that immediately drew the wrath of Brexit supporters, EU officials said that the prime minister had suggested she was “ready to consider” a longer transition period in the hope of breaking open the deadlocked talks. Downing Street sources later said that such a move – during which the UK would abide by EU rules but have no say in them – had not been ruled out.

May’s concession on Wednesday came as she pleaded for “courage, trust and friendship” from both sides in her speech to EU leaders. But despite EU council president Donald Tusk’s earlier demand for “new facts” to unlock the negotiations, the prime minister did not offer fresh proposals, instead highlighting the progress already made and the hurdles that remained.

“We have shown we can do difficult deals together constructively. I remain confident of a good outcome. The last stage will need courage, trust and leadership on both sides,” she told her EU counterparts.

The prime minister appeared unable to persuade her audience that she could back her conciliatory tone with a substantial offer. Antonio Tajani, the president of the European parliament, said she had offered nothing new in her speech.

“I did not pick up anything substantially new in terms of content,” he said. “I was listening to Mrs May. It was the tone of someone who want to reach an agreement [but] there is no change in content.”

Tajani added that May appeared neutral on the idea of extending the transition period by a year, to the end of 2021. Another source familiar with the talks said that she told EU leaders that she was open to an extension of the transition “in a cautious way”.

An extension of the Brexit transition period would likely mean the UK needed to make additional budget contributions to the EU on top of its £39bn divorce bill.

An EU source said that the leaders had decided over dinner that they would not call a special Brexit summit in November, as sufficient progress in the talks had not been made. The source said: “The EU27 leaders stand ready to convene a European council, if and when the union negotiator reports that decisive progress has been made. For now, EU27 is not planning to organise an extraordinary summit on Brexit in November.”

‘I did not pick up anything substantially new’ – Antonio Tajani. Photograph: Anadolu Agency/Getty Images

Even as EU leaders expressed their disappointment, news of May’s openness to an extension sparked an angry response from Brexit supporters in the UK, with Nigel Farage claiming that the news “may mean we never leave at all”. He told BBC’s Newsnight programme: “The problem isn’t Brexit, the problem is the prime minister.”

The EU has suggested that extra time to seal a comprehensive trade deal could offer some further reassurance that the backstop solution for avoiding a hard border on the island of Ireland would not be used.

An offer of an extension clause on the 21-month transition period had already been made by the EU during the recent secretive round of talks, as first revealed by the Guardian. But the idea has been rejected by Eurosceptic Conservative backbenchers because it would leave the UK subject to EU rules and paying into the budget while having no say over how its money is spent.

EU leaders dined on pan-fried mushrooms, fillet of turbot cooked in wheat beer and a trio of fruit sorbets while they discussed their next steps on Brexit following a 15-minute meeting with May, who was not invited to dinner.

The two sides remain deadlocked over the Irish backstop, a fallback plan to prevent a hard border on the island of Ireland in the absence of any trade agreement.

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.

EU sources said there would be no compromise on a permanent backstop, despite British hopes of securing a temporary arrangement to avoid being tied into the EU customs union indefinitely.

The Irish taoiseach, Leo Varadkar, took a front-page Irish Times report of a bombing to the leaders’ dinner to stress the point that peace was more important than trade. Varadkar talked to leaders about a 1972 bombing of a border customs point to help convey his point about the dangers of a hard border, the Irish Times reported on Wednesday night.

May’s cabinet have told her they will not accept either an indefinite backstop – or one that leaves Northern Ireland in a different regulatory regime.

In response to suggestions of an extension to the transition period, Diane Dodds, a DUP MEP, tweeted it “doesn’t do anything to actually change the backstop [and] offers no reassurance”.

All very well, but this doesn't do anything to actually change the backstop, as it would be in the legal text of the withdrawal agreement. Therefore it does not address any concerns, it offers no reassurance. https://t.co/cCoJCrbC8g — Diane Dodds MEP (@DianeDoddsMEP) October 17, 2018

In a bid to solve the problem, the EU is searching for language that would convince the British that the backstop would never be used. May reiterated that the government believes the key is to secure the right future trading relationship, which would make border checks unnecessary. The European commission, however, has long insisted that it will only discuss the details of a trade deal after the fraught Irish backstop question is resolved.

A UK official speaking in Brussels insisted the UK still hoped a Brexit deal could be “wrapped up in the autumn”.

Shadow chancellor John McDonnell said an extended transition period would increase uncertainty for business when they were already worried about what might happen. He told ITV’s Peston show there was a “coup working its way through the Conservative party” that had left negotiations “floundered”.

“Everyone I talk to now – business leaders, investors, trade union leaders all of them are saying the uncertainty and the insecurity at the moment means decisions are not being taken about long-term investment,” McDonnell said.

The EU’s chief Brexit negotiator, Michel Barnier, warned at the start of the EU leaders summit in Brussels that the negotiators needed “much more time” to complete a deal. Arriving to brief leaders at the summit on Brussels, Barnier told reporters: “We continue to do the work in the next weeks calmly and patiently.”

Dalia Grybauskaitė, the president of Lithuania, warned that the talks were being set back by the disunity in May’s cabinet, saying: ““We do not know what they want, they do not know themselves what they really want – that’s the problem.”

However, a senior UK official insisted: “The prime minister has a clear mandate to negotiate and there is a clear position which has been set out, which the cabinet is firmly backing.”

EU leaders arriving in Brussels repeatedly stressed the importance of making progress. Emmanuel Macron, the French president, said the need for progress was “urgent”. Mark Rutte, the Dutch prime minister, said he was “cautiously optimistic” that an agreement would be made “in the coming weeks” on the Irish border.

May flew to Brussels after the weekly session of prime minister’s questions in Westminster, at which Labour leader Jeremy Corbyn sought to exploit her party’s deep divisions over Brexit.

“The Conservative party has spent two years arguing with itself instead of negotiating a deal in the public interest,” Corbyn told a sometimes raucous House of Commons. “And now, just days before the deadline, they’re still bickering amongst themselves.”