Jeremy Hunt has seized on Labour’s split, claiming to European foreign ministers it proved that only concessions to win round Conservative rightwingers will get the Brexit deal through the Commons.

During a frenetic day of lobbying in Brussels, the foreign secretary privately counselled his EU counterparts that the opposition could not be relied upon, even if the government pivoted to backing a customs union.

The peeling away of seven MPs from the Labour party was said by Hunt on Monday to illustrate that the Brexit deal would only be saved by addressing Tory and DUP concerns about the “indefinite” nature of the Irish backstop, which could keep the UK in a customs union to avoid a hard Irish border.

Stephen Barclay, the Brexit secretary, and the attorney-general, Geoffrey Cox, are expected to return to Brussels on Wednesday, after Monday’s two hours of talks over the backstop with the EU’s chief negotiator, Michel Barnier.

It is understood that Cox laid out what he would need to revise his legal opinion. The two sides are exploring the possible legal means to reconcile the gap between the Irish protocol’s description of the backstop as “temporary” and its “indefinite” legal effect.

But while Downing Street is banking on a change in Cox’s legal opinion persuading Brexiters to back the deal, there appears to be little hope of the withdrawal agreement itself being reopened as promised by the prime minister in January in response to the historic defeat of her deal with the EU by 230 votes.

On Tuesday, the French EU affairs minister, Nathalie Loiseau, reiterated the refusal of the 27 member states to renegotiate, and expressed those doubts voiced in many capitals about the government’s strategy.

She also warned that Brussels would not simply delay Brexit to avoid a no deal, urging the prime minister to think again about the future relationship so as to garner cross-party votes.

“We are waiting for Mrs May to come with some precise proposals because she said that she had some things to tell us,” Loiseau said. “Now time is pressing. We are about a month away from the UK’s exit, an exit which will take place on March 29 because she hasn’t given any signals that there will be a delay.”

The French minister added: “We are in favour of a delay either for some days for technical reasons, [or] if it’s for political reasons there has to be a real advance on something that is supported by a majority in the British parliament which corresponds to our red lines, our negotiating directives.

“If we have to talk about a reformulation of our future relationship it’s entirely possible to do that. If it’s about reopening the withdrawal agreement we have all already said that this point is not negotiable”

Michael Roth, Germany’s minister for Europe, echoed those comments, adding that the UK had not come forward with any new thinking in recent days.

“An extension would only make sense if we have new substantial ideas on the table. Otherwise there’s no point. And of course we would look at such a suggestion closely should the British in fact decide to ask for an extension,” he said.

“But this is solely the responsibility of the British, we can’t make such a suggestion. And then we have to unanimously vote on it. In the end the deadlines are very clear: if there is a substantial extension, for example past the 1 July, then of course there will also have to be elections in Great Britain, but I don’t want to speculate about this.”

Quick Guide Why extend the Brexit transition period? Show Will the proposal solve anything? The mooted extension to the transition period is a new idea being put forward by the EU to help Theresa May square the circle created by the written agreement last December and the draft withdrawal agreement in March.

That committed the UK and the EU to ensuring there was no divergence between Northern Ireland and the Republic of Ireland.

But it also, after an intervention by the Democratic Unionist party, committed the UK (not the EU) not to have any trading differences between Northern Ireland and Great Britain.

The problem is that these are two irreconcilable agreements. They also impinge on the legally binding Good Friday agreement, which brought peace to Northern Ireland and in some senses pooled sovereignty of Northern Ireland giving people a birthright to be Irish or British or both.

If the UK leaves the EU along with the customs union and the single market then the border in Ireland becomes the only land border between the UK and the EU forcing customs, tax and regulatory controls. The backstop is one of three options agreed by the EU and the UK in December and would only come into play if option A (overall agreement) or option B (a tailor-made solution) cannot be agreed by the end of transition. The Irish have likened it to an insurance policy. The new EU idea is to extend the transition period to allow time to get to option A or B.

But an extension is problematic for Brexiters and leave voters, who want the UK to get out of the EU as soon as possible.

The Irish and the EU will also still need the backstop in the withdrawal agreement, which must be signed before the business of the trade deal can get under way. Otherwise it is a no-deal Brexit.

Extending the transition into 2021 would mean another year of paying into the EU budget. Britain would have to negotiate this but it has been estimated at anywhere between £10bn and £17bn. Staying in the EU for another year would also mean continued freedom of movement and being under the European court of justice, which Brexiters would oppose.

Of the British calls for a renegotiation, Roth said there was “no point in abstractly demanding changes or to make demands, which are completely unacceptable for us”.

He said: “There can be no limit to the backstop, there can’t be an automatic expiration of the backstop. Therefore we will continue to be open to dialogues, after all we want to find a sensible solution, we want to prevent a hard Brexit.

“It would be the worst, both for Great Britain as well as for the EU27. But right now I do not see the necessary willingness to budge on the part of the British and this doesn’t make things easier because time is running out.”

A spokesman for the commission said the prime minister would be meeting with the European commission president Jean-Claude Juncker on Wednesday evening. “We cannot accept a time limit to the backstop or a unilateral exit clause and further talks will be held this week to see whether a way through can be found that could gain the broadest possible support in the UK parliament and respect the guidelines agreed by the European council”, the spokesman said.

In an interview with Politico, Hunt nevertheless claimed to expect a significant breakthrough in the next few days, insisting it would be “definitely more than a clarification” while falling short of a rewriting of the withdrawal agreement.

The prime minister has until now been demanding a time limit on the backstop, a unilateral exit mechanism or its replacement with alternative arrangements.

The considerable gap between British expectations and the stance of the EU has many worried in Brussels.

Hunt, who met seven EU foreign ministers on Monday and the prime minister of Flanders, nevertheless said a swift resolution was necessary “for the sake of sanity of the population of Britain and indeed of Europe”, adding that the end was in sight. The Commons is set to hear from the prime minister on the progress of her negotiations next Wednesday.

The foreign secretary offered a sober analysis of what he would regard as a success. “Success will be if in 10 years’ time people who voted against Brexit, people in that 48%, are able to say, ‘You know what, it hasn’t been as bad as I feared and the UK is flourishing’,” Hunt said.