Theresa May will abandon attempts to strike a Brexit deal with Labour if no cross-party agreement can be struck within one week.

The prime minister has bowed to pressure to finally set a deadline for ending the talks with Jeremy Corbyn if necessary – deciding the Labour leader must be on board with seven days, a government source said.

If Labour agrees not to block the withdrawal agreement bill, it would then be put to the Commons – but the government will “move in another direction” if no guarantee is given, The Independent was told.

The deadline was set after Monday’s talks went better than expected. The prime minister’s spokesperson described them as “serious and constructive”.

Until now, Downing Street has refused to say how long it would allow negotiations with Labour to continue – despite mounting Conservative anger at the tactic.

Ministers are already resigned to taking part in next month’s European elections – and a likely thumping by Nigel Farage’s new Brexit party – because of the lack of progress.

Farage launches his new Brexit Party: in pictures Show all 10 1 /10 Farage launches his new Brexit Party: in pictures Farage launches his new Brexit Party: in pictures Nigel Farage speaks at the launch of his new Brexit Party's campaign for the European elections Reuters Farage launches his new Brexit Party: in pictures Brexit Party candidate Annunziata Rees-Mogg, sister of Conservative MP Jacob Rees-Mogg, speaks at the launch AFP/Getty Farage launches his new Brexit Party: in pictures A supporter waits for Farage to speak AFP/Getty Farage launches his new Brexit Party: in pictures Supporters wait for Farage to speak AFP/Getty Farage launches his new Brexit Party: in pictures Farage's socks Reuters Farage launches his new Brexit Party: in pictures Farage and prospective candidate Annunziata Rees-Mogg wait at the launch AFP/Getty Farage launches his new Brexit Party: in pictures Supporters listen as Farage speaks AFP/Getty Farage launches his new Brexit Party: in pictures Free T-shirts for all attendees AFP/Getty Farage launches his new Brexit Party: in pictures Posters on the seats for supporters of the Brexit Party AFP/Getty Farage launches his new Brexit Party: in pictures A safety sign is pictured AFP/Getty

Despite warmer words after Monday’s talks, the two sides remain far apart on Labour’s demands for a customs union and on how to ensure any deal is not ripped up by Boris Johnson, or another Brexiteer new prime minister.

It is unclear what moving in “another direction” would entail, but Ms May is likely to tack back to trying to win the backing of the Democratic Unionist Party.

The source said that the cabinet agreed there was “a need to get on with it” and that the impasse must “come to a head” if no progress was apparent by the middle of next week.

It is understood that the ultimatum – which the prime minister believes is necessary to allow her party to set out a firm stance before the European elections on 23 May – has been delivered to Labour.

Introducing the bill to ratify a deal might still allow Brexit to be completed in time to prevent MEPs taking their seats in Brussels at the start of July.

However, to move ahead, Ms May needs to be certain that Labour will not vote down the legislation immediately – forcing her to prorogue parliament and risk a Queen’s Speech that could accelerate her departure from No 10.

Even the prime minister’s “plan B”, further “indicative votes” to try to establish a Commons majority behind one Brexit option, is believed to rest on Labour support.

For the first time, Ms May’s spokesperson, discussing Tuesday’s cabinet meeting, referred to the talks with Labour heading “towards a conclusion”.

“Cabinet received an update on the Brexit talks with the opposition, including the negotiations last night which were serious and constructive,” he said.

“Further talks will now be scheduled in order to bring the process towards a conclusion.

“Cabinet also discussed the need to secure safe passage of the withdrawal agreement bill as soon as possible in order to deliver upon the result of the referendum.”