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So was it all just theatrics; a show designed to allow Theresa May to say she had fought to the very last? Or was the sudden collapse of Brexit talks over the weekend proof that a no deal is now, as the DUP claims, “probably inevitable”?

Only time will tell. But there isn’t much of that left, and things are starting to look a little fraught. Despite a last-minute Sunday afternoon dash to Brussels by the Brexit secretary, Dominic Raab, unresolved “serious issues” meant a breakthrough remained beyond negotiators’ grasp.

The nub of the problem remains how to avoid a hard border between Northern Ireland and the Republic without instead creating barriers between Northern Ireland and the rest of the UK.

The EU’s proposed solution is for Northern Ireland to in effect remain in the single market and customs union for as long as necessary, which the government has rejected. May repeated on Monday that no solution that “threatens the integrity of our United Kingdom” could be acceptable.

Instead, Britain has suggested that the whole country stays in a customs union with the EU, but for a limited time only – which the EU has rejected as both too complicated and (if only temporary) not good enough.

The PM is cornered. Pro-leave cabinet members are facing backbench calls to resign to force a change of policy or leader, with former Brexit secretary David Davis calling the plan to keep the UK in a customs union “completely unacceptable”.

At the same time, the DUP – on whose backing May’s majority relies – say the whole border issue is an “EU con trick” and are threatening to bring down the government if Brexit means Northern Ireland is treated differently from the rest of the UK.

Meanwhile, pro-remain Tory MPs have promised to vote down any Chequers-style deal because it would wreck the economy, and Labour is demanding MPs be given an opportunity to debate the government’s border backstop plans before this week’s EU summit in Brussels.

And the EU27, while willing to help May over the line if they can, show no signs of budging from their no-cherry-picking fundamentals. Not for the first time, it’s not looking pretty.

What next?

Technically, an agreement is in sight. Politically, thanks to May’s weakness at home, it’s a long way off. All negotiations are now on hold, with the prime minister due to address EU27 leaders at dinner at their summit on Wednesday.

The bloc had, however, demanded “maximum progress” on the border problem by this week as the price for a November summit at which a deal was to be formally signed off. That could now become a “no-deal” summit to address the consequences of the UK crashing out of the bloc.

Prospects for a deal could, therefore, be pushed back to a December summit. For the time being, EU diplomats appear relatively relaxed about this possibility and are prepared – up to a point – to wait and see whether May can sell her Brexit plan at home. All now hangs on whether she can.

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In the Guardian, Matthew d’Ancona says that even if Theresa May does reach a historic agreement with the EU, she faces a backlash from the DUP and possibly her cabinet, followed by political annihilation:

Parliament is entitled to a meaningful vote on the outcome of the negotiations. If MPs reject that deal, the government has 21 days to make a fresh statement to the Commons about its intentions. Next, the prime minister has until 21 January to present an amended agreement. And after that? Well, then things start to get really vague … With each passing day, the shining palace that leave promised us in 2016 looks more and more like a dilapidated Victorian folly. Hectically, crazily, the nation is careering towards the unknown. I’d say it could go either way – if it were remotely clear what those ways might be.

Ian Jack reckons those who most loudly trumpet their patriotism would quite happily break up Britain, as long as they get their beloved Brexit:

How strange that unionism should be threatened by the Orange halls of the six counties and Conservative clubs in the shires: the kind of places where people sing Land of Hope and Glory without irony and believe Britain is a free country like no other … If the price of Brexit was Scottish independence, 77% of English Conservatives would pay it. If the price was the collapse of Northern Ireland’s peace process, 73% of them would likewise be content. Among leave voters in Northern Ireland, overwhelmingly unionist, that figure rose to 87%, while 86% thought a yes vote in a second Scottish independence referendum would be a worthwhile price for Northern Ireland to leave the EU. The fact is, Brexit matters more to them.

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A veteran observer concludes simply: