The deadline, agreed at a meeting in Paris on Wednesday evening, comes as the bloc’s chief negotiator Michel Barnier told Mr Johnson to stop “pretending” to negotiate.

On Wednesday evening French president Emmanuel Macron – who has taken the hardest line against the UK – met with Antti Rinne, Finland’s prime minister and the current holder of the rotating EU Council presidency.

“If the UK wants to discuss alternatives to the existing Brexit agreement then these must be presented before the end of the month,” Mr Rinne told reporters after the meeting in which the deadline was agreed.

“We are both concerned about what is happening in Britain right now and the confusion that is going on from there to Europe.

“If no proposals are forthcoming, I believe that quite a few European leaders agree with the position. Then it’s over. Now is the time to come up with clear presentations and make them verifiable.”

The new deadline gives Mr Johnson 12 days to produce proposals to replace the Irish backstop, which he has said he wants to scrap and replace with something else. Although Mr Macron and Mr Rinne do not speak for the whole EU, the deadline has weight given Finland holds the rotating presidency – which is charged with coordinating the views of member states.

Officials in Brussels are concerned the prime minister is wasting their time and playing out talks for as long as possible without presenting proposals – possibly with an eye on an upcoming election.

The bloc’s chief negotiator Mr Barnier told the European parliament earlier in the day: “Almost three years after the UK referendum, I don’t think we should be spending time pretending to negotiate. I think we need to move forward with determination.”

EU officials told The Independent last week that they were losing patience – and that they feared they were being “led up the garden path” by the UK negotiators.

Reports suggest ideas brought to Brussels by UK negotiators have amounted to the same as the old agreement, with the section on the Irish backstop simply crossed out in the text. UK sources have also reportedly suggested full proposals are being deliberately held back to the last minute for timing reasons.

he EU side has been briefing that Mr Johnson experienced a “penny dropping moment” during his meeting with EU boss Jean-Claude Juncker earlier this week in Luxembourg.

According to the accounts of EU officials quoted in the Financial Times, Mr Johnson appeared not to understand that his proposals for Northern Ireland to stick to EU food and livestock regulations after Brexit would not resolve the ongoing impasse over customs arrangements at the border.

An official described Mr Johnson “slumping” in his chair at the lunch in Luxembourg, as his Brussels counterparts said that the plan for common “sanitary and phytosanitary” (SPS) rules on the island of Ireland would not do away with the need for customs checks on the vast majority of goods crossing the border.

According to the newspaper, one official said the PM turned to chief negotiator David Frost and Brexit secretary Stephen Barclay and said: “So you’re telling me the SPS plan doesn’t solve the customs problem?”

Speaking in the same European parliament debate on Wednesday, Jean-Claude Juncker, the European Commission president, said of a meeting with Mr Johnson in Luxembourg on Monday: “I said to Prime Minister Johnson that I have no emotional attachment to the backstop but I stand by the objectives it’s designed to achieve. I called on the PM to come forward with operational proposals in writing for practical steps which would allow us to achieve those objectives.”

Although it has not presented full proposals, the UK has come forward with one idea: a theoretical veto for Northern Ireland on any backstop replacement. This plan was, however, dismissed by parliament Brexit chief Guy Verhofstadt on Wednesday as “a permanent instrument for blackmailing” the EU during negotiations.

MEPs in the European parliament on Wednesday afternoon approved a resolution that says they support an extension of Article 50 to prevent a no-deal Brexit.

The Independent understands that there was controversy on the parliament’s Brexit steering group over whether the resolution should include “preventing a no deal” as one of the possible justifications for an Article 50 extension. Some MEPs on the group – thought to be close to Emmanuel Macron – attempted to have the justification removed, leaving only a general election and second referendum as reasons for a further delay. A source said the thinking behind the attempt to remove the line was that it undermined the EU negotiating position.

The attempt failed – meaning the parliament supports an extension in virtually all circumstances to stop the UK crashing out. While the parliament’s position on an extension is purely symbolic, because the question of one is down to EU leaders on the council, the episode highlights the existence of divisions on the EU side over the question of further delays.

But despite the setback in the parliament, those looking for a tougher line on the UK appear to be making headway with member states. Addressing the issue of whether an extension would be granted, Finnish prime minister Mr Rinnie said: “Something must happen that extra time can be granted. If there is no genuine new solution in sight, there is no prerequisite for granting additional time.”

The new deadline set by the leaders complicates efforts to avoid a no-deal Brexit; parliament has legislated to force Mr Johnson to demand an extension of Article 50 if no deal has been signed by 19 October – the day after the next meeting of the European Council.

Mr Johnson spent the afternoon calling around EU leaders. A Downing Street spokesperson said: “This afternoon the prime minister spoke to European Commission President Juncker, European parliament President Sassoli, Cypriot President Anastasiades, and Latvian Prime Minister Karins.

“The prime minister and President Juncker discussed the positive and constructive conversation they had in Luxembourg on Monday, and their shared determination to reach a deal.

“The prime minister updated the other European leaders on the progress of the Brexit talks to date and reiterated that, when the UK leaves the EU on October 31, his preference is that we do so with a deal. He spoke about the work that was under way to find an alternative to the backstop that protects both the Good Friday/Belfast Agreement and the integrity of the single market.”