Theresa May’s prospects of cobbling together a cross-party majority to convince EU leaders to grant a short Brexit delay next week appear to be slipping away after Labour claimed she had failed to offer “real change or compromise” in talks.

The prime minister made a dramatic pledge to open the door to talks with Labour on Tuesday after a marathon cabinet meeting.

But after two days of negotiations and an exchange of letters on Friday, Labour issued a statement criticising the prime minister for failing to offer “real change or compromise”.

“We urge the prime minister to come forward with genuine changes to her deal in an effort to find an alternative that can win support in parliament and bring the country together,” a spokesperson said.

The pessimistic note came after May wrote to the European council president, Donald Tusk, on Friday morning, asking for Brexit to be delayed until 30 June, while cross-party talks continue.

Even before Labour’s statement, EU politicians responded with bemusement to her failure to offer a concrete plan for assembling a coalition behind a workable deal – increasing the risk that they will take a tough line at next Wednesday’s summit.

May’s letter suggested that the UK was preparing to field candidates in European parliamentary elections on 23 May if no deal could be reached. But there was considerable opposition in parts of Europe as France signalled its readiness for a no-deal Brexit on 12 April if there were no significant new British proposals, and won the support of Spain and Belgium, according to a note of an EU27 meeting seen by the Guardian.

While Germany took a more conciliatory tone, the diplomatic cable revealed that the French ambassador secured the support of Spanish and Belgian colleagues in arguing that there should only be, at most, a short article 50 extension to avoid an instant financial crisis, saying: “We could probably extend for a couple of weeks to prepare ourselves in the markets.”

European leaders already wary of the prospect of a long extension were further unsettled on Friday by a tweet from the Conservative MP Jacob Rees-Mogg, who said that the UK should disrupt the EU from within in the event of a significant delay.

Jacob Rees-Mogg (@Jacob_Rees_Mogg) If a long extension leaves us stuck in the EU we should be as difficult as possible. We could veto any increase in the budget, obstruct the putative EU army and block Mr Macron’s integrationist schemes.

“The functioning of the EU is a central element as how we proceed,” an EU official said. “The tweet of Jacob Rees-Mogg showed what they are capable of.”

Meanwhile, the shadow Brexit secretary, Keir Starmer, said that the government was refusing to countenance changes to the political declaration negotiated with Brussels.

Instead, May’s de facto deputy, David Lidington, wrote to him with a proposal that the two sides agree a separate memorandum dealing with the issues Labour had raised.

But Downing Street rejected Labour’s characterisation of the government’s stance. “We have made serious proposals in talks this week, and are prepared to pursue changes to the political declaration in order to deliver a deal that is acceptable to both sides,” a spokesperson said.

“We are ready to hold further detailed discussions this weekend in order to seek any such changes in the run-up to European council on Wednesday. The government is determined to work constructively to deliver the Brexit people voted for, and avoid participation in the European parliamentary elections.”

May has said, including in her letter to Tusk, that if she cannot strike a Brexit deal with Labour, she hopes the two sides can devise a process for parliament to choose between several Brexit options - and agree to abide by it.

Negotiations between Labour and the government began on Wednesday, after the prime minister said she hoped to find a cross-party deal that could win a parliamentary majority, instead of relying on Tory and DUP votes alone.

She had staged three House of Commons votes on her Brexit deal, but failed to win a majority each time, with the DUP and a string of pro-Brexit rebels voting against her.

After Tuesday’s cabinet meeting, members of the soft-Brexit “Gaukeward squad”, including the justice secretary, David Gauke, and the work and pensions secretary, Amber Rudd, believed the prime minister had made a decision that she would rather sacrifice some of her red lines – including customs union membership – rather than countenance a no-deal Brexit.

But Friday’s breakup of talks without progress being made will increase the alarm about the risk that the EU27 might refuse any further extension next Wednesday and push the UK out without a deal rather than endure more political paralysis.

Labour figures involved in the negotiations were taken aback at the paucity of the government’s offer, which was in stark contrast to the serious engagement displayed, in particular by Lidington and May’s chief of staff, Gavin Barwell, a day earlier.

EU diplomats have been watching the talks closely, for evidence of the emergence of a stable majority for any kind of Brexit deal.

Before the negotiations stalled, France’s secretary of state for European affairs, Amélie de Montchalin, told the Guardian in a statement: “The European council took a clear decision on 21 March … Another extension requires the UK to put forward a plan with clear and credible political backing.”

France’s robust approach, and the unravelling of the cross-party talks, dented the value of the pound on foreign exchanges, with sterling briefly dropping below $1.30 against the dollar after Labour’s statement.

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Areas covered in Lidington’s letter are understood to include customs arrangements, workers’ rights and environmental standards, but to be aspirational, rather than representing firm new commitments on the government’s part.

The prime minister conceded in her letter to Tusk that the government would now have to make preparations for participating in May’s European parliament elections – but still hoped to ratify a Brexit deal, and pass the requisite legislation, in order to leave before that, by 22 May.

“The government will want to agree a timetable for ratification that allows the United Kingdom to withdraw from the EU before 23 May 2019 and therefore cancel the European parliament elections, but will continue to make responsible preparations to hold the elections should this not prove possible,” she said.

Backbench MPs led by Yvette Cooper hope to force the prime minister to request a much longer extension. Their backbench-led bill is expected to finish all its parliamentary stages on Monday, which would allow the House of Commons to vote on a motion aimed at forcing her to make the request.

Corbyn and his negotiating team had been under pressure to insist on a confirmatory referendum as the price of any deal with the government – although that would be all but impossible for the Conservatives to sign up to, given the opposition among their own MPs.