At 5.30pm on Tuesday, British and EU negotiating teams gathered in a room on the fifth floor of the European Commission’s Berlaymont headquarters.

On the UK side were Steve Barclay, the Brexit Secretary, Geoffrey Cox, the Attorney General, senior advisor Olly Robbins, and Sir Tim Barrow, the UK ambassador to the EU.

Across the table were chief negotiator Michel Barnier, his deputy Sabine Weyand, senior Task Force advisors Stéphanie Riso and Nina Obermaier and officials from the commission’s legal service.

After 90 minutes of talks, they repaired to the 13th floor for a dinner that lasted just under two hours.

Over a mi-cuit tuna starter, a main course of cod, and fondant au chocolat blanc for dessert, both teams got to grips with the UK’s first formal request for legally binding changes to the Irish backstop.

By all accounts the evening did not go well.

The European Commission formally described the talks as "difficult" - one stage beyond "robust" in the lexicon of negotiation euphemisms.

"There was no progress," says one EU official. "Everybody’s in stalemate."

In fact, the EU side was startled at what they perceived as London demanding a sizeable re-write of the Withdrawal Agreement.

British sources dispute this characterisation.

London has been looking for safeguards on the Irish border that, officials say, would equalise the burden of the backstop, which they say currently falls squarely and unfairly on the UK side.

Redressing the balance would, according to London, permit Geoffrey Cox to overturn the legal advice he gave to British Prime Minister Theresa May last November that the Irish Protocol could keep the UK in the backstop indefinitely.

However, Tuesday’s meeting graphically exposed how far apart both sides were.

On Wednesday, EU ambassadors were given a detailed briefing by Sabine Weyand of the previous night’s encounter.

While this was very much the EU’s take on things, it was clear there was deep dismay at what Mr Cox was proposing.

Having accepted that the EU would not countenance a straightforward unilateral exit clause from the backstop, nor an expiry date, critics said London was now looking for a way to peel away from the logic of the backstop through the novel use of the arbitration process.

How would this work?

The Withdrawal Agreement creates a Joint Committee of EU and UK representatives to implement and manage the provisions of the deal over time.

Under the Withdrawal Agreement both sides commit to "make every attempt, through co-operation and consultations, to arrive at a mutually satisfactory resolution" if a dispute arises.

But if it is not possible to resolve the dispute through the Joint Committee, then it goes to arbitration.

The treaty provides for an overall arbitration panel of 25 highly qualified and independent international experts – ten recommended by the EU, ten by the UK and the final five chosen jointly.

A sore point for the UK is that, if the dispute is over a point of EU law, then an arbitration panel does not get involved.

Only the European Court of Justice can arbitrate on matters of EU law.

The problem with the backstop, from a UK point of view, is that it is ultimately bound up with EU law.

The determination of whether it can be superseded by a free trade agreement, and/or "alternative arrangements" (ie, technology) intrinsically relates to whether or not that trade deal does away with the need for checks and controls on the Irish border.

And since those checks and controls are part and parcel of the EU’s customs and single market rulebook, the extent to which the trade deal obviates those checks and controls is only a call that the ECJ can make.

That would, in theory, rule out a role for an independent arbitration panel – populated by UK appointees – in determining whether or not the backstop can fall away.

However, what if the issue was not over single market rules, but if the UK felt that the EU was not pulling its weight in the negotiations?

The EU says the treaty obliges both sides to act in good faith and use best endeavours. Furthermore, deciding whether both sides were actually pulling their weight was ultimately a political and not a question.

However, in order to make it a legal question, Cox – according to Sabine Weyand’s analysis – introduced a new concept: one of "reasonableness".

Michel Barnier and Sabine Weyand

According to Weyand, this is a legal term which is used in commercial law, but not one that is applicable to international arbitration. (Alex Barker in the Financial Times sourced the concept to Victorian England, and the notion of the Man on the Clapham Omnibus, the mythical figure who embodied the fair-mindedness needed to determine if someone had acted "reasonably" in, say, negligence cases.)

"It’s about trying to find a legal mechanism to settle what will be a eminently political question down the line," says one official familiar with the negotiations.

In other words, Cox wanted to inject a concept that would give the UK the ability to appeal to the arbitration panel – and not the European Court of Justice – in the hope that it would rule that the trade negotiations were stuck, that the UK had acted with "reasonableness" and was therefore entitled to walk away from the backstop.

"The point is that Cox doesn’t want the ECJ involved in the adjudication on whether or not we’ve reached agreement," says the official.

"That’s why he’s trying to look at ‘reasonableness’, because that would not affect EU law."

The move took the EU by surprise.

"It was a frontal British effort to try to create an exit from the backstop through this notion of manipulating arbitration," says one EU diplomat.

"It's a new approach in relation to the backstop not being indefinite."

However, Cox’s proposal was that if such a scenario unfolded, and the international arbitration panel did indeed conclude that the UK could walk away from the backstop, there would then be a fallback, what has been reported as a "mini backstop".

According to one source: "This would be limited to what was strictly necessary to avoid infrastructure at the border."

At the meeting of EU ambassadors, Weyand interpreted this as meaning only checks on animal and plant health and food safety, the so-called sanitary and phytosanitary (SPS) rules, as well as checks on prohibited goods.

In other words, if the UK was granted permission to walk away from the backstop, it would still facilitate checks on goods going from Great Britain to Northern Ireland – so as to avoid infrastructure on the land border – but only SPS controls.

It would not include controls on the movement of goods. That would mean checks on those goods crossing the land border.

In terms of customs, according to Weyand, the UK’s suggestion was that the EU carry out these checks "away from the border".

One senior Irish source was scathing: "This misunderstands the whole construction of the backstop. It misunderstands the overall objective, as per the Joint Report [of December 2017] and the protocol. It’s about the unique situation on the island of Ireland, North-South cooperation, and the Good Friday Agreement.

"This would be turned into a shriveled up and utterly distorted version of that."

According to reports, Michel Barnier flatly rejected the proposal.

Not only did it partially dismantle the backstop itself, it also outsourced the remit of the ECJ to an international body.

Britain's Attorney General Geoffrey Cox

Furthermore, officials believed that Cox was moving the goalposts and departing from the position outlined by Theresa May when she met Jean-Claude Juncker on 19 February.

"The commission had understood from May that the main source of concern was that the commission and the EU would be fickle and too comfortable with the backstop, and wouldn’t use ‘best endeavours’ in negotiating it," says one official.

"The commission was happy to clarify that and provide assurances on best endeavours in that context."

Cox had a further eye-catching suggestion.

This was that the backstop was potentially in breach of the European Convention on Human Rights (ECHR) because under the backstop, the citizens of Northern Ireland would be subject to EU single market rules yet not represented in the making of those rules.

It is understood Cox glancingly referred to Article 3 of the protocol to the ECHR which commits signatories to ensuring "the free expression of the opinion of the people in the choice of the legislature".

To EU officials this took the backstop into entirely different terrain.

"This is about attacking the legality of the backstop, the same backstop which has been negotiated by Her Majesty’s best team of lawyers," says one official.

"That didn’t really help the dynamics."

None of the concerns about representing the people of Northern Ireland had been raised in Cox’s initial legal advice back in November.

Officials in Brussels suspect this was a last minute gambit in order to win over the DUP.

Indeed, the day after the Brussels dinner, the DUP’s Brexit spokesman Sammy Wilson told the Northern Ireland Select Committee: "We would be subject to rules made in Brussels for a wide range of activities in Northern Ireland without any opportunity to have an input into them … and we would find ourselves increasingly removed from laws which are made in Westminster and superseded by laws which are made in Brussels".

DUP's Brexit spokesman Sammy Wilson

EU sources counter this by saying that the UK is entitled, through the Joint Committee, to outsource the co-management of the backstop to Stormont as it sees fit.

One EU diplomat also points out that Norway is subject to the rules of the single market, but does not send elected representatives to the European Parliament.

British officials have long complained that the backstop has an asymmetrical risk: to London the burden of the backstop falls on the UK, with the risk that it could be indefinite, so Cox’s objective was to rebalance the risk in a legally binding manner.

The EU has been shifting towards providing legally binding assurances, through a Joint Interpretative Statement that sets out the obligations to conclude a free trade deal and look at alternatives to the backstop in quick time.

However, Geoffrey Cox appeared to go well beyond this.

Essentially he was attempting to incentivise the EU through the threat of not having a backstop at all.

"It looked like he wanted to create equal risk for the EU," says one source.

"By not having a backstop at all, this becomes the counter-risk to having a backstop forever."

The overall mood darkened further.

EU ambassadors on Wednesday discussed the potential blame game if the talks did not deliver a breakthrough. By Friday it had started.

On BBC Radio 4’s Today Programme, Foreign Secretary Jeremy Hunt said: "[In] future generations, if this ends in acrimony, people will say the EU got this wrong, and I really hope they don't."

On Friday afternoon at the strongly Leave-voting fishing port of Grimsby, Theresa May said: "Just as MPs will face a big choice next week, the EU has to make a choice too. We are both participants in this process. It is in the European interest for the UK to leave with a deal ... My message to them is: now is the moment for us to act."

Ahead of May’s speech, Michel Barnier called another meeting with EU ambassadors.

There was a sombre mood. There was a feeling that May was preparing to blame the EU if talks broke down irretrievably.

"People were upset to hear things were not moving forward and the Brits were not playing ball," says one official briefed on the meeting.

"People were annoyed at the blame game, and felt that the prime minister’s speech had not helped at all. If that was the message, make it in person, make it directly, make it with figures that support your claim that you’re about to see a change with your MPs."

Following the meeting Michel Barnier published a series of tweets.

The EU was now offering a "legally binding interpretation of the Brexit Withdrawal Agreement.

Essentially, he was spelling out what was already in the agreement, with a fresh offer that the "best endeavours" obligation to find ways of replacing the backstop could be boosted within a Joint Interpretative Statement - a legally binding mechanism - that was "actionable" before the arbitration panel.

What the EU was offering was a more legally robust version of the Tusk-Juncker letters of January, spelling out that the backstop was intended to be temporary and that both sides would seek to use all means to replace it as soon as possible.

👇 I briefed EU27 Ambassadors and EP today on the ongoing talks with #UK. Following the EU-UK statement of 20 Feb, the EU has proposed to the UK a legally binding interpretation of the #Brexit Withdrawal Agreement. Most importantly: — Michel Barnier (@MichelBarnier) March 8, 2019

In fact, EU leaders had considered the offer of such an instrument in December but had hesitated. Now Barnier was putting it on the table.

One official explained: "The arbitration panel already has all these features - it’s just giving it more ammo. It was something we’d already contemplated in December, but were reluctant. The [Tusk-Juncker] letters came out as letters so we needed to elevate those."

Stefaan De Rynck, an EU Task Force spokesman, defended the offer on Twitter, saying the "best endeavours" clause was now more "actionable" if the UK felt the EU was not pulling its weight: "This is not recycling; it is an additional legal reassurance in case the EU fails to deploy best endeavours to conclude an agreement that replaces the backstop."

However, the arbitration panel could only be invoked if the EU was only not pulling its weight or seriously engaging on the issue.

If the EU decided that a free trade agreement was not in a position to supersede the backstop on the grounds that it undermined the integrity of the single market, then only the ECJ could make the final call on that.

In another tweet, Mr Barnier said: "[The] EU commits to give UK the option to exit the Single Customs Territory unilaterally, while the other elements of the backstop must be maintained to avoid a hard border. UK will not be forced into customs union against its will."

Despite the UK's demand for a unilateral exit clause to the backstop - the Single Customs Territory, in treaty-speak - this was not it.

The Protocol already gives the UK the option to exit unilaterally, but only so long as Northern Ireland remains.

The key phrase is: "The provisions of this Protocol shall apply unless and until they are superseded, in whole or in part, by a subsequent agreement".

So the price the UK would have to pay for walking away, would be reverting to the original Northern Ireland-specific backstop Theresa May rejected one year ago, something quickly recognised by the DUP’s Nigel Dodds.

"Nothing new in what Barnier is offering," he said on Twitter.

"This is a retreat back to the proposal of an Northern Ireland only backstop previously rejected by all sides in the House of Commons."

It was a dramatic end to a difficult week, with both sides now staring at another heavy defeat of the Withdrawal Agreement in the House of Commons next week.

Officials in Brussels describe Barnier’s offer as "defensive", brought about by sense of shock over what Geoffrey Cox was proposing, and the exaggerated expectations in Westminster over what the EU would be prepared to offer.

In a sense the EU did blink - as the UK commentariat have always predicted they would - but the blink only delivered what the EU has said repeatedly would be the maximum they could offer, and it goes nowhere near far enough for the DUP and the European Research Group.

Technical talks will continue over the weekend. Barnier had a long-standing family arrangement to take his two sons to Dublin for the Ireland France Six Nations clash.

That trip was looking iffy earlier in the week. The fact that it is back on is good news for the Barnier family, but bad news for the Brexit negotiations.