THE last week has seen the start of a turbulent Brexit endgame. On Tuesday, the Commons rejected Theresa May’s withdrawal agreement for the second time. The Commons also amended May’s fudged no-deal motion, on Wednesday, to a straightforward rejection of no deal – which May voted then against.

Despite these defeats, on Thursday, May’s own motion on delay – a short one if her deal passes at the third attempt or a longer, unspecified one – was passed but only thanks to opposition parties’ support, with several Brexiter Cabinet ministers voting against. Yet, despite the ever deeper splits in May’s chaotic government and party, she has not given up.

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What happens next depends partly on whether May’s deal can scrape through at the third attempt in the next couple of days – that would mean buying off the DUP, and the support of a number of Labour pro-Brexit rebels to cancel out Brexiter Tories opposing May to the end.

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But the EU’s leaders are now a powerful player in these complex end-game dynamics. If May’s deal is rejected again, there will be little time for indicative votes in the Commons on other Brexit options before the European Council meets on Thursday and Friday. Such votes might only happen after the summit – when May’s deal could return a fourth time too.

The EU’s leaders are frustrated and appalled at the UK’s chaotic, irresponsible politics of Brexit. They all have other key EU priorities and their own national political concerns. And the European Parliament elections loom large – a moment when, for most EU leaders (if not in Hungary and Poland), right-wing populist parties must be held in check to avoid a major negative fall-out for the EU.

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The simplest outcome for EU leaders, in many ways, would be if May’s deal passed at the third attempt and she asked the EU27 for a two to three month delay to get necessary legislation through the Commons (which may well prove difficult in itself) before a new Brexit day in late May or June. But if the unloved deal is rejected again, then no-deal or longer delay looms.

European Commission president Jean-Claude Juncker, France’s President Emmanuel Macron and several others emphasise that the UK must say what a delay is for before the European Council agrees. Even then, there would be conditions. Extending Article 50 requires unanimous agreement of the EU27, giving them a moment of maximum power and leverage.

There’s a presumption that the EU would grant a two to three month delay in the face of a looming no-deal cliff edge. But, as the Irish finance minister said on Friday, there’s not much appetite for simply rolling the cliff edge forward three months. Equally, the EU does not want the chaos of the UK crashing out of the EU on March 29 – doubtless returning cap in hand for emergency talks within weeks or even days – just as the European Parliament election campaigning is taking off.

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In a no deal scenario, it’s not even clear if the EU would offer the same deal again or instead a more basic set of agreements to iron out some of the worst chaos. The EU doesn’t want to be held responsible for no-deal. But the UK’s crisis is clearly its own responsibility. So a hard ball EU refusal of an extension might seem unlikely but can’t be ruled out.

Or faced with the Commons still only knowing what it’s against not what it’s for, the EU might choose – as Council President Donald Tusk has suggested – to offer a long extension, perhaps nine months or so. This has the advantage of putting Brexit on the back burner for the EU. It might also be used tactically by European leaders so that May could have a fourth attempt, post-summit, to get her deal through – threatening Brexiters that a long delay makes a soft Brexit or no Brexit much more likely (surely the case).

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BUT such an extension would come with conditions. It would surely mean the UK would have to participate in the European Parliament elections. There are also serious concerns in EU capitals at the UK playing political games with other EU issues while it remains a member state. EU leaders would want minimally a political commitment from the UK to take a backseat in decisions on appointments of the new presidents of the Commission and European Council and on future budget talks.

If May’s deal is defeated again, the EU will surely demand Westminster explains what a longer delay is for – an election, a People’s Vote or some substantive process of coming to a decision on what sort of Brexit the UK wants. Yet an election could be held within a short extension. And even a soft Brexit could be done fairly swiftly, if Westminster made a clear choice on that. So a long delay makes sense mainly if it’s for a People’s Vote (on remain versus May’s deal) or if it’s the EU’s best idea for getting Brexit off its agenda for now or allowing a last ditch chance for May’s deal to go through.

And EU leaders, given their current position of maximum leverage before granting delay, may not even agree delay at their summit this week. They haven’t yet discussed delay, and their own differences of view on that, at 27. They might make a provisional decision at the summit while insisting Westminster provides clarity. Only then, with no-deal just a few days away, might they formalise their offer which the Commons would have little choice but to accept, if it came as late as the March 27 or 28.

The damaging and chaotic Brexit pantomime at Westminster exists in a vortex where it seems the rest of the EU barely exists. But the EU’s leaders are about to be centre stage for the next two weeks. And if the Commons wants to have a say, not just take what it’s offered, it had better get its act together very fast indeed.