Angela Merkel has warned her country’s business leaders that the Brexit negotiations are in danger of collapse.

With talks in Brussels at an impasse with just months to go before a deal needs to be agreed, the German chancellor made a rare intervention at a conference in Frankfurt.

She told major players in the world of German finance on Tuesday: “We don’t want the discussions to break down. We will use all our force and creativity to make sure a deal happens. We don’t want these negotiations to collapse. But we also can’t fully rule that out because we still have no result.”

The EU says it needs a deal to be struck on the withdrawal agreement covering citizens’ rights, the £39bn divorce bill and the Irish border, along with the political declaration on the future deal, by November at the latest.

The German chancellor has generally played a backseat role in the talks, preferring to intervene only at crunch points at EU summits.

EU leaders are due to meet in Brussels in October, but an emergency summit is being pencilled in for 13 November in case the negotiations require an extra few weeks for agreement to be made.

The leaderswill gather at a summit in Salzburg later this month where the EU27 are planning a “carrot and stick” approach to Brexit, offering Theresa May warm words on the Chequers proposals to take to the Conservative conference alongside a sharp warning that they need a plan for Northern Ireland within weeks.

The twin statements from the EU leaders would seek to give the British prime minister some evidence of progress in negotiations on the future trade deal as she seeks to fight off the threat of rebelling MPs.

However, under the plans being discussed among the 27, a shot would be fired across May’s bows on the issue of a backstop for Northern Ireland, an issue on which officials and diplomats are becoming increasingly frustrated.

Where do the Brexit negotiations stand? Read more

May committed in December, and again in March, to agree on a plan for avoiding a hard border between Ireland and Northern Ireland. This would come into force if a trade deal or bespoke technological solution that could do the same job was not available by the end of the transition period, on 31 December 2020.

The British cabinet was told on Tuesday that May’s struggling Chequers plan received a “warm and positive” response from European capitals during a Brexit diplomatic offensive over the summer.

Downing Street suggested the prime minister would increase her direct lobbying of European leaders as negotiations entered their final stages, even as she battles to save her proposals from fierce criticism in the UK.

Quick guide Will the Chequers agreement survive? Show Hide Who dislikes the Chequers agreement and why? Noisiest in their opposition are Tory Brexiters, not least David Davis and Boris Johnson, both of whom quit the cabinet in protest. They argue that the promise to maintain a common rulebook for goods and other continued alignment will mean a post-Brexit UK is tied to the EU without having a say on future rules, rather than being a free-trading independent nation. Labour has also disparaged the proposal, expressing deep scepticism about the so-called facilitated customs arrangement system. What about the EU? Brussels has sought to stay positive, but has deep concerns about elements of the plan viewed as overly pick-and-mix, and thus potentially incompatible with EU principles. Michel Barnier, the EU’s chief Brexit negotiator, says he opposes both the customs plan and the idea of alignment for goods. He also makes plain his contention that the Chequers plan contains no workable idea for the Ireland-Northern Ireland border. But at the same time the EU has been careful to not entirely dismiss the proposals, raising the possibility it could accept some adapted version. Who supports the agreement? Officially, May and her cabinet, though even here the backing can seem lukewarm at times. Asked about Chequers, the home secretary, Sajid Javid, said it was the government’s plan “right now”, indicating alternative ideas could be considered. Is it doomed? Even May’s allies concede it will be a hugely difficult task to get the plan through parliament. Damian Green, the PM’s close friend and former de fact deputy, described the process as “walking a narrow path with people chucking rocks at us from both sides”. On the remain side of the Conservatives, the former education secretary Justine Greening called the Chequers plan “more unpopular than the poll tax”, saying May should start again from scratch. If anything can save the plan – and it’s an outside shot – it will be a combination of the hugely tight timetable and the fact that, as yet, no one else has yet produced a plan with a better chance of being accepted by parliament. What happens next? On 20 September, an informal gathering in Salzburg, Austria, will provide a snapshot of current EU thinking. Then, 10 days later, the Conservative conference could show the Chequers plan is holed below the waterline. If it survives these tests, the proposals will then reach the crucial EU summit Brussels on 18 October, with something final needed, at the very latest, in the next two months. PETER WALKER

The move adds weight to the theory that the government plans to go over the head of the European commission directly to the EU27 to secure a deal.

Downing Street did not dismiss this suggestion. May’s official spokesman said: “The negotiations are taking place with the commission; we have always respected that fact. But equally this is a decision that at the end of the process will be taken at a political level by the European council, so you can obviously expect a continued and strong engagement with fellow European countries.”

The EU27 fear the British are seeking to push back the resolution of the Irish border issue into the transition period, after the UK has left the EU on 29 March 2019.

Tempers have flared in recent negotiations over the issue and member states want to send a clear warning that they are not willing to let the issue remain unresolved.

Senior EU diplomats and officials admit that the central tenets of the Chequers proposals, involving a common rulebook on goods and an unprecedented customs arrangement, are dead in the water.

However, it is believed that the “zero tariffs, zero quota” offer made by Donald Tusk, the European council president, in March, along with fresh thinking on how to facilitate customs checks to reduce friction at the border, could be developed and packaged as a substantive counter-offer. “There is a lot that can be done to minimise checks,” said an EU diplomat. “What is an internal market in goods? A lot of this is semantics.”

The EU leaders will meet in the Austrian city on 19 and 20 September. May is likely to have the opportunity to present her thoughts to leaders over dinner on the first evening, with the leaders then discussing the issues over lunch the following day.

EU sources said the Brexit plan and the summit itinerary had yet to be signed off, but there was a consensus among the member states that May should be given some help before what is likely to be a fiery Tory conference less than two weeks later.