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It was another rollercoaster week, beginning with widespread predictions that Boris Johnson’s Brexit plan was all but dead as No 10 admitted there was little prospect of a deal before 31 October and bitter recriminations flew.

But as the government set up a Westminster Brexit showdown by calling MPs to sit in an exceptional Saturday session on 19 October, the day after this week’s EU summit, the prime minister and the Irish taoiseach, Leo Varadkar, met on the Wirral.

To most people’s surprise, the two men emerged from more than three hours of talks agreeing that there was a “pathway to a possible deal”, prompting the chief EU negotiator, Michel Barnier, and the Brexit secretary, Stephen Barclay, to meet in Brussels.

The EU subsequently agreed to enter so-called “tunnel discussions” on a possible deal based on Johnson’s acknowledgement – a big concession from his previous position – that there could not be a customs border on the island of Ireland.

With the Northern Ireland unionists of the DUP promising to be “flexible” and the EU talking up the prospects of a Brexit extension beyond 31 October if necessary, many – including the culture secretary, Nicky Morgan, – saw the chances of a deal as promising.

Quick Guide Why is the Irish border a stumbling block for Brexit? Show Counties and customs Inside the EU, both Ireland and Northern Ireland are part of the single market and customs union so share the same regulations and standards, allowing a soft or invisible border between the two.

Britain’s exit from the EU – taking Northern Ireland with it – risks a return to a hard or policed border. The only way to avoid this post-Brexit is for regulations on both sides to remain more or less the same in key areas including food, animal welfare, medicines and product safety. The 'backstop' in Theresa May's Withdrawal Agreement was intended to address this - stating that if no future trade agreement could be reached between the EU and the UK, then rules and regulations would stay as they are. This has been rejected by Brexit supporters as a 'trap' to keep the UK in the EU's customs union, which would prevent the UK striking its own independent trade deals. There are an estimated 72m road vehicle crossings a year between Northern Ireland and the Republic of Ireland, and about 14% of those crossings are consignments of goods, some of which may cross the border several times before they reach a consumer. Brexit supporters say this can be managed by doing checks on goods away from the border, but critics say it will be difficult to police this without any physical infrastructure like border posts or cameras, which could raise tensions in the divided communities of Ireland.

Interactive: A typical hour in the life of the Irish border Photograph: Design Pics Inc/Design Pics RF

A weekend of talks, however, ended with Barnier saying there had been no major breakthrough. A timely deal looked “impossible”, he said, warning that negotiations may have to continue as UK’s Irish border plans represented an “untested” risk.

The British proposal takes Northern Ireland out of the EU customs union, with the UK agreeing to enforce the bloc’s customs rules and tariffs on goods moving from Britain to Northern Ireland and a rebate system to compensate affected businesses.

With Johnson edging steadily towards the numbers needed to pass a deal in the Commons as more hardline Eurosceptics and pro-deal Labour MPs indicated they could back a new agreement, momentum began to grow.

Dampening expectations somewhat, Finland’s prime minister, Antti Rinne, warned there was not enough time left for a formal agreement before the summit began on Thursday and Barnier said a deal this week remained “difficult, but possible”.

But after the EU’s chief negotiator set Johnson a deadline of midnight on Tuesday to concede to EU demands and agree to a customs border in the Irish Sea if he wanted a deal by Saturday, EU and UK sources said the two sides were on the brink of success – despite misgivings in Paris and Berlin at the rush to a deal.

What next

It depends what happens at the summit. The prime minister has made a series of major U-turns, giving EU officials hope he will table a legal text based on the February 2018 Northern Ireland-only backstop rejected by Theresa May as a constitutional outrage.

De jure, Northern Ireland would be in the UK’s customs territory, but de facto it will be in Britain’s, is the idea. (A similar deal was blown up by the DUP and the hardline ERG group last year, but both seem to be giving Johnson more leeway.)

But Johnson could also walk out on the summit and attack Brussels for intransigence. Or the two sides could agree to further negotiations next week, opening up the possibility of a second EU summit, perhaps on 29 October, to sign off on a deal. Either way, a new extension beyond 31 October looks inevitable.

Ideally, Johnson would probably like to put a deal to parliament on 19 October come what may. But France and Germany want more time, and fudge, delay and prevarication have been the watchwords throughout the Brexit process. There is no reason to doubt they will not be now.

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In the Guardian, Rafael Behr argues that any Johnson-style deal will sow the seeds of future confrontation with the EU:

Johnson envisages a future in which the UK does not shadow EU market rules. The greater the regulatory divergence on either side of a border, the harder that border has to be. Zoom out further and you see a statement of intent by the UK to gain a competitive edge by undercutting its former EU partners. The original economic conception of Brexit is to make Britain a low-cost lure for investment. Brussels doesn’t like the sound of that. May was persuaded of the need for strategic proximity to the rest of Europe and saw economic alignment as a necessary condition to achieve that. Johnson’s view is different. In his world, the UK can develop an economic model conceived by people who despise the EU, alongside a foreign policy in which UK-EU relations are unaffected. He seems to think that EU leaders do not notice or do not mind. He is mistaken. There are no reserves of personal trust in the prime minister and he has hitched himself to a doctrine of cut-throat competition that, whether he understands it or not, sets the UK on an economic collision course with Brussels. Even with a deal, the consequences will be messy.

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Brexit legal commentator David Allen Green is absolutely not wrong: