What will happen next with Brexit now MPs are back in Westminster?

Brexit Explained: Cross-party talks to break the deadlock will resume this week but a solution to the current crisis seems a long way off

MPs will return to Westminster on Tuesday after an Easter break that offered them a precious few days away from the Brexit crisis that has gripped parliament in recent weeks.

While Theresa May’s agreement with the EU to delay Brexit until 31 October means the immediate pressure to approve an exit deal has been lifted, the problem has not gone away.

The prime minister is desperate to avoid the UK having to take part in European parliament elections on 23 May – almost three years after the public voted to leave the EU.

The extension offered by the EU gives the UK the ability to leave the bloc earlier than October if parliament ratifies a withdrawal agreement. The government says this would allow the UK to cancel the EU elections if a deal is passed by 22 May.

In a bid to achieve this, May sought talks cross-party talks with Labour to try to break the deadlock in parliament. The negotiations are set to resume this week but the two sides are still some way apart, with ministers having so far refused to accept Labour’s demand for a permanent customs union with the EU.

An agreement is not impossible but it appears unlikely given the current state of the discussions. Last week, a Labour spokesperson admitted there were “substantial differences” between the two parties. But with neither side wanting to be seen to scupper the talks, they could drag on for some time.

May has said that if the two parties cannot agree on a way forward, they will instead draw up a series of options for MPs to vote on. The prime minister has insisted that the government “stands ready to abide by” whatever the Commons decides – but only if Labour does that same. It is far from certain that Jeremy Corbyn will agree to do so.

Then there is the question of whether MPs would vote for any of the potential outcomes. When two rounds of “indicative votes” were held earlier this month, no option won a majority. However, a proposal for a customs union with the EU was only narrowly defeated and could pass if put to another vote.

If the negotiations with Labour end without agreement and parliament fails to vote for any Brexit plan, May might be forced to try to turn back to her own party, and her Commons partners in the DUP, in one last-ditch bid to secure approval for her withdrawal agreement.

If that fails, as seems likely, then the chances of a fresh referendum or a general election will rise significantly.

May’s own future is just as uncertain as that of Brexit. Under current Conservative Party rules, the prime minister is safe from a no-confidence vote because only one can be held each year and she saw off an attempt to topple her last December.

Many Conservative MPs want to change this. On Tuesday, the 1922 Committee that represents backbench Tories will meet to discuss proposals to allow another confidence vote to be held this year.

If they decide that this should go ahead, May could be ousted within weeks – leaving the fate of Brexit even more uncertain. MPs could soon be longing for another break.