Labour has accused Theresa May of failing to offer any substantive changes to her Brexit deal in cross-party talks, as Downing Street’s hopes of a breakthrough in time to avoid taking part in European parliamentary elections waned.

Brexit talks resumed on Tuesday between a team of ministers and shadow ministers. But Labour sources said the government team again appeared unwilling to countenance changes to the political declaration, which sets out the UK’s future relationship with the EU.

Instead, ministers offered alternative ways of giving reassurance about the issues Labour has raised, such as on environmental standards and workers’ rights, including through redrafting the withdrawal act implementation bill (WAB) and tweaking separate planned government bills.

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Downing Street continues to insist that it hopes to secure parliamentary ratification of a Brexit deal in time to avoid the UK having to participate in next month’s European parliament elections.

The government has been considering tabling the WAB as a way of breaking the Brexit deadlock, but Labour has rejected the idea. “There’s a sequence; you have got to start with a different deal,” said a source.

After the talks, which involved the cabinet ministers David Lidington and Steve Barclay and their Labour shadows, Jeremy Corbyn blamed the government’s refusal to compromise on central issues such as membership of a customs union for the failure to make significant progress.

“We’ll continue putting our case but quite honestly there’s got to be change in the government’s approach. They cannot keep on just regurgitating what has already been emphatically rejected three times by parliament, there’s got to be a change,” Corbyn said. “We have a window of opportunity to bring about that change so I hope the government recognises that.”

However, Downing Street sought to blame a lack of urgency on Labour’s side for the impasse. May’s spokesman said she had told her cabinet on Tuesday morning that talks with Labour had been “serious but had also been difficult in some areas such as in relation to the timetable of the negotiations”.

A No 10 source said the root of the tension was a feeling that Labour was prepared to drag its heels, with less inclination to avoid the EU elections than the Tories, who are desperate to cancel them.

“Progress needs to be made urgently,” May’s spokesman said, adding it was “reasonable” to conclude that the government wanted to make progress faster than Labour.

One Labour source said the ministers involved in the talks appeared to be less engaged than in recent meetings, and suggested the government had been distracted by the latest attempt to oust May.

The executive of the 1922 Committee met on Tuesday night to discuss amending Tory party rules, which currently state a leader cannot face a second no-confidence motion within a year of the previous one. Changing the party’s rules to allow a no-confidence motion at any time would make it easier to force May out.

May defeated an attempt to challenge her in December, meaning she is safe from an official vote for at least another seven months.

There is a suggestion the limit could be shortened to six months, meaning she could face a contest in June. But one senior committee officer said there would be an attempt to remove the time limit altogether, as there was an appetite to get on with removing May as soon as possible.

If the rules are changed, at least 15% of Conservative MPs – 47 of them – would need to send letters to Sir Graham Brady, the chair of the committee, in order to trigger another confidence vote. This threshold is likely to have already been met, given the scale of discontent within the parliamentary party.

The officer said opinion on the committee was finely balanced as there were roughly equal numbers of remainers and Brexiters, but feeling was “building up against May,” because of the Conservatives’ dire poll numbers.

No decision is expected to be made on Tuesday; but the committee plans to meet again on Wednesday, ahead of a full meeting of Tory backbenchers at which many are likely to vent their frustration about the approach of the prime minister – who has already promised to step down if her Brexit deal is agreed.

Without Labour support, the government is unlikely to risk bringing back the WAB, which parliament must pass in order to ratify May’s Brexit deal. Tabling it would help to avoid the Speaker’s stricture that the government cannot hold another “meaningful vote” on an unchanged deal.

May’s spokesman said members of the cabinet were united in agreement that they need to “secure safe passage for the WAB through parliament as soon as possible, in order for the UK to complete the ratification for its orderly departure from the EU”.

But introducing it would be a high-stakes gamble unless the government is confident of securing considerably more support. May’s deal was rejected for a third time last month, by a majority of 58.

If the WAB is rejected at its second reading – MPs’ second opportunity to vote on it – the government could not bring it back in the current parliamentary session. Ministers believe that could allow backbench MPs to table amendments and shift the course of Brexit – pushing for a customs union, for example.

One government source suggested May appeared to be paving the way for reluctantly accepting a customs union at the cabinet meeting on Tuesday.

But in order to be amended a bill must pass its second reading and Labour sources suggested the party would only be willing to offer its support if May first agreed to compromise. Without the backing of Labour, the government appears unlikely to be able to shift the parliamentary arithmetic enough to assemble a majority.