Donald Tusk’s team was waiting in the wings as the European Council President held his 45-minute meeting with Leo Varadkar.

As they waited they were monitoring Tweets coming in from Brexiteers, some of whom were laying down the law ahead of Theresa May’s visit to Brussels the following day. One, from Nadine Dorries MP, caught their attention.

"A legally binding limit won’t pass in Parliament," Dorries declared.

"The Prime Minister would suffer a further crushing defeat. It’s open the withdrawal agreement, remove the backstop, or No Deal."

The uncompromising language evoked a sinewy pleasure among officials. They knew what was coming next.

Moments later, next to the Taoiseach, Donald Tusk delivered the headline-grabbing words.

"I’ve been wondering what that special place in hell looks like, for those who promoted Brexit, without even a sketch of a plan how to carry it out safely," he said.

The remarks prompted a deluge of odium, and outraged headlines in the UK.

"What possessed him?," asked The Sun, after calling Mr Tusk a "staggering fool", under the headline "To Hell With EU".

"What did he hope to gain from such a tantrum?" the editorial asked

The answer, according to several sources, was he felt it was time to deliver some home truths.

"It was from the heart," says one source. "That’s the truth of it. That’s what he feels.

"He looks at the abrogation of responsibility and he sees that the Brexiteers have largely operated in an accountability-free zone while saying absolutely whatever they like about anybody and everybody across Europe.

"The minute anybody says ‘boo!’ back to them they act like a horrified victim of assault and battery."

While the "special place in hell" remark did not appear in earlier drafts of the statement, Tusk’s team knew full well that strong language was on the cards – and so did Leo Varadkar.

The Taoiseach and the Irish delegation were appraised in advance of the thrust – if not the detail – of Mr Tusk’s broadside.

The furore over the "hell" remarks actually eclipsed the more important signal: his oft expressed sadness at Brexit and forlorn hope that it could be somehow reversed ("You may say I’m a dreamer…but I’m not the only one", from June 22, 2017) was finally confronted with reality.

"The facts are unmistakable," he said. "At the moment, the pro-Brexit stance of the UK Prime Minister, and the Leader of the Opposition, rule out this question.

"Today, there is no political force and no effective leadership for Remain. I say this without satisfaction, but you can't argue with the facts."

At a stroke Tusk was abandoning his own romantic hopes and out of a sense of accumulated frustration, letting the Brexiteers have it with both barrels.

The former Polish prime minister has been no stranger to blunt remarks that have gone against the grain of mainstream EU sentiment.

At the height of the refugee crisis Tusk told the European Parliament. "Declaring solidarity is always greeted with applause, while calling for responsibility and common sense - hardly ever. Practising solidarity is a lot harder than preaching it … The first commandment today is the restoration of control on the EU´s external borders."

In December 2017, he described the European Commission’s plans for mandatory refugee quotas as "ineffective" and "highly divisive". The EU migration Commissioner Dimitris Avramopoulos described the remarks as "anti-European".

Just days after Donald Trump’s inauguration in Washington, Tusk once again raised eyebrows in a letter to EU leaders, highlighting "worrying declarations by the new American administration [that] make our future highly unpredictable," and which seem "to put into question the last 70 years of American foreign policy".

According to one official: "President Tusk is an extremely careful politician. When he says something he is very well aware of what will happen afterwards. At times, he has been dreadfully criticised for what he said. But in retrospect people looked back and said, actually he was right."

Other sources in Brussels take a different view.

"There is a certain sense of frustration that we who work on this issue can share," says one EU diplomat. "But I thought the timing was not the best because you knew it would be misunderstood. But at least he got it off his chest."

Another EU source says: "From a communications perspective I wouldn’t have used such language because then it’s all about the catchphrase. You lose the part about who exactly you’re talking about."

Ultimately, the episode reveals President Tusk’s pessimism that a No Deal crash out can be avoided. Had a genuine solution been in sight, Tusk would not have taken the risk of derailing it by using such intemperate language.

Officials say that in the meeting between Tusk and Varadkar, the Taoiseach was the more optimistic of the two that the parliamentary machinery in the House of Commons would ultimately steer the ship away from the rocks of No Deal.

Tusk was not convinced. The following day there was little in his meeting with Theresa May that raised his confidence that the Withdrawal Agreement could be salvaged.

The pair met for just under an hour, and while Mrs May chided Mr Tusk over his "hell" remarks and he said he stood by them, she did not bring forward any concrete proposals on what kind of legally binding changes to the backstop she was looking for.

Meeting PM @theresa_may on how to overcome impasse on #brexit. Still no breakthrough in sight. Talks will continue. pic.twitter.com/vn2CVybc1j — Donald Tusk (@eucopresident) February 7, 2019

So, what exactly is Theresa May’s strategy?

She has managed to re-open talks on the backstop. She and Jean-Claude Juncker will meet again before the end of Feburary, Michel Barnier and Stephen Barclay, the Brexit secretary, will meet on Monday.

In London, the Working Group on Alternative Arrangements is continuing to look at technology, expiry dates and unilateral exit clauses.

Ahead of the prime minister’s visit to Brussels on Thursday, British officials were coy as to what precise changes Theresa May would seek.

"We’re not specific on surgery or an additional mechanism," said one official. "We’re clear that changes to the Withdrawal Agreement are required, but we’re open as to how that can be achieved. But it has to be legally binding."

However, according to recent and previous discussions with senior British figures, it is clear that the emphasis will be on a unilateral exit mechanism – where the UK can walk away from the backstop – with a renewed focus on the bilateral relationship between the United Kingdom and Ireland.

The pathway can be traced back to the Mansion House speech of March 2018, which in turn paved the way for Theresa May’s Chequers White Paper.

The question of Theresa May’s bid to have an exit mechanism is intimately linked to the issue of how to reconcile alignment and freedom when it comes to Britain’s future trade relationship with the EU.

Let’s go back to the Mansion House speech, nearly one year ago.

London pitched it as much more conciliatory and realistic than the hard Brexit-flavoured Party Conference (October 2016) and Lancaster House (January 2017) speeches.

At the Mansion House, Mrs May hinted at the UK accepting a much higher degree of regulatory alignment with the EU than previously considered.

"As with any trade agreement," she said, "we must accept the need for binding commitments – for example, we may choose to commit some areas of our regulations like state aid and competition to remaining in step with the EU’s."

Trade should be across "as frictionless a border as possible" in order not to "damage the integrated supply chains our industries depend on".

The EU, she said, already had a tailored approach to free trade agreements. Market access depended on the "respective interests of the countries involved" and the EU was quite happy to vary the level of access to the single market, depending on the obligations those neighbouring countries were willing to undertake.

Why couldn’t the UK enjoy something similar?

This could be done through a "comprehensive system of mutual recognition", with Britain making a "strong commitment that its regulatory standards will remain as high as the EU’s."

Both sets of "regulatory standards will remain substantially similar in the future."

UK law would not be identical to EU law, "but it should achieve the same outcomes".

The House of Commons might decide to pass an identical law if exporters convinced them it made sense "to have a single set of regulatory standards that mean they can sell into the UK and EU markets".

But if MPs decided not to achieve the same outcomes as EU law, "it would be in the knowledge that there may be consequences for our market access".

This, then, was the blueprint of Chequers.

The UK would decide itself to align with the EU through the so-called "common rulebook" when it came to goods, with an ambiguously defined role for the European Court of Justice on policing that rulebook (essentially, although it was never admitted, the single market acquis).

The UK would go its own way on services.

Chequers also revived the so-called customs partnership idea, floated in August 2017, with the UK maintaining the EU’s common external tariff where appropriate, and acting as customs collecting authority for the EU where the UK’s tariffs were lower.

Behind the scenes, as the Mansion House speech and the Chequers embryo were taking shape, there was a furious battle between Downing Street and Brexit hardliners in the European Research Group (ERG).

May was leaning towards closer alignment through a customs partnership, Jacob-Rees Mogg was adamant that technology would do the trick on the Irish border through maximum facilitation, or Max Fac.

"It’s a battle between Theresa May and 60 people," confided one British negotiator at the time. "This is about her and 60 or 70 people in her party who have a very particular and different vision."

The conflicting models were, in fact, both gateways to very different ways of realising Britain’s future relationship with the EU.

Theresa May’s customs partnership idea was focused on a legal mechanism that would deal with both the customs and regulatory alignment dilemmas in a much more holistic way. This was necessary: the EU’s customs union and single market intimately intersect when it comes to how duties are paid, and how regulatory compliance is monitored.

"Max Fac, on the other hand, takes a dozen or so processes," explained the negotiator at the time, "and tries to come up with individual solutions to each of them – what can be moved away from the [Irish] border, and all that sort of thing. That’s the difference between the two: one is a fundamental concept, the other is a series of fixes."

In other words, Theresa May’s customs partnership idea was essentially a gateway to frictionless trade that would solve both the Northern Ireland issue, and the supply chain issue (indeed, in her Mansion House speech she explicitly linked the two problems for the first time).

The customs partnership would get rid of customs formalities at the border and allow automotive supply chains to continue unhindered, while the regulatory issue could be dealt with through "mutual recognition" of standards and a "strong commitment" that the UK and EU would have "substantially similar" regulations in the future.

It wasn’t that Theresa May didn’t believe in technology. It was simply that she knew it wasn’t yet available. So, in the meantime this hybrid customs-regulatory model would have to do, even if it meant the UK opting for high-alignment, and even if it hindered the UK’s ability to negotiate free trade agreements in goods.

"Theresa May is steadfastly convinced of the customs partnership idea and all the high alignment that comes with it," insisted the British negotiator.

"Fine, in ten or 15 years the technology might be there, and we could be benefitting from all these third country trade deals. But there’s a hell of a journey in the meantime, so, she’s saying to herself, I’ve got to take a very pragmatic approach."

What then happened?

Theresa May’s ideas were fused in the Chequers White Paper. Brexiteers hated it because it tied the UK to the EU’s single market (through the "common rulebook") and essentially prevented the UK from negotiating trade deals based on goods.

The EU disliked it because it split the four freedoms, by separating off services, and because there was no one-size-fits-all concept of "mutual recognition" of standards.

As a result Theresa May was forced to salvage a chunk of her customs partnership idea and then lobby the EU to turn the Northern Ireland-specific backstop into a "temporary customs arrangement" that would cover the whole of the UK.

The EU resisted, but eventually agreed as the Withdrawal Agreement negotiations reached a climax.

There was the proviso that this UK-wide customs backstop would be superseded only if a free trade agreement removed the need for any customs checks, or related controls, on the Irish border.

On the regulatory side, in a backstop scenario, Northern Ireland would be subject to specific provisions of the EU’s single market rulebook.

So that brings us to the current impasse: the temporary customs arrangement, which is part of what the backstop has become, and which Theresa May asked for, has, according to the UK Attorney General Geoffrey Cox, the potential to become indefinite.

UK Attorney General Geoffrey Cox (right) in Dublin with Irish counterpart Seamus Woulfe

The EU’s view is that it’s only indefinite so long as the future trade deal does not solve the border issue. Exiting the backstop is not time-driven, it’s event-driven.

But in the UK the backstop is now presented as a "trap", and that’s what Theresa May wants to change.

This brings us back to the link between the Mansion House/Chequers on the one hand, and the current "alternative arrangements" mission.

British sources accept that weaving a way through the tangle of issues will not be easy, especially given that Ireland and the EU are adamant that the Withdrawal Agreement cannot be reopened, and the backstop cannot be changed.

The emphasis, therefore, is on "rebalancing", and Geoffrey Cox has the lead role.

According to London’s analysis, the backstop unfairly "traps" the UK because it is in the Withdrawal Agreement and is therefore legally binding.

The future relationship, which is supposed to give the UK a pathway out of the backstop, is delineated in the Political Declaration, which is not legally binding.

This means, according to London, that there is an asymmetry that much be addressed. Yes, the Withdrawal Agreement commits both parties to use their "best endeavours" to find an agreement that supersedes the backstop. But London now believes that, having agreed the text in November, it is not enough.

"There needs to be some combination of sufficient further assurances to rebalance this asymmetry between the political commitments and the legal text," says a British source.

"That plays on this basis that there is willingness to find alternative ways of doing it over time. It will depend on finding a way on the [EU] side to give that sufficient trust about the long-term commitment, so you can find that line between the commitments to finding a solution that works, but not getting stuck in this particular [backstop] solution".

In other words, Theresa May is looking for some mechanism or leverage that will allow the UK to declare that the EU is not abiding by its best endeavours promise, both in terms of effort, and in terms of what the future relationship will look like.

And here we get back to the Mansion House/Chequers ideas.

In the Mansion House speech, Theresa May made the essential point that the UK was too big and too economically powerful to have an off-the-shelf trade deal with the EU, ie neither Canada nor Norway.

At the same time, the two economies would be have to be close. "A deep and comprehensive agreement with the EU will therefore need to include commitments reflecting the extent to which the UK and EU economies are entwined."

For the EU, this is all fine. Except, that the UK cannot enjoy that deep entwinement if it is not signing up to EU’s rules and subject to the monitoring of the European Commission and the enforcement of the European Court of Justice.

However, London still believes that the UK is too big, and that this needs to be somehow legally reflected in the Withdrawal Agreement. "You have to have a degree of confidence," says the source, "that there is going to be willingness to consider things that are not membership of the single market and customs union in the future."

What would those options be? They are found in Chequers.

"It comes back to the need to think about the future relationship," says the source. "It’s the alignment model of Chequers. The EU, for its political reasons said no to that. But actually, we have to get back to a conversation about it. You look sector by sector, how you can get to a trade model that is as frictionless as possible."

In other words, the future relationship will have to be an integrated economic model, but not as integrated as the status quo, and the degree of integration will depend on the sector involved.

The EU will argue that only a free trade deal that has high-alignment on customs and goods will guarantee that it can supersede the backstop. If alignment is lower, there is friction at the Irish border.

However, London will argue that Chequers gets both sides close. And both sides must now have the discussion about how close that relationship can be.

The problem for London is, again, that that discussion is not resolved in a legal way in the Withdrawal Agreement.

"There’s still this sense of the asymmetry on the way this is set up," says the source. "How can you, when push comes to shove, have any great assurance that there will be that level of engagement on finding an alternative, when you have this legal form that you can fall into and can’t get out of?"

How would this "rebalancing" work in a legal way? The answer appears to be, from London’s viewpoint, a time limit or exit clause which acts as a harder incentive for all sides to find that sweet spot in the future relationship.

"If you’re committed to finding alternative arrangements," explains the source, "and you’re committed to finding a future relationship that works, what’s the problem with potentially having a time limit on this particular set of arrangements with the backstop? You can then agree on an alternative set-up or something that looks very similar.

"There will need to be something. Something that tips the balance towards more certainty that you will be able to walk away from it if there hasn’t been a good faith attempt, or another acceptance of other arrangements that would solve it."

That something would more likely be in the form of an exit clause rather than an expiry date, which would be arbitrary.

The more fundamental point is strengthening that sense of the legal power of being able to call time, say sources, "or having a fair arbitration as to when this is being done".

There are several immediate problems with this line of argument.

Firstly, these issues were thrashed out over and over again in the negotiations. The demand for a time limit, back in Dominic Raab’s day, was countered by an offer of a review mechanism.

London complained that the review would have to be mutually agreed, therefore Britain could not walk away unilaterally. The EU argued that the question of whether or not the free trade agreement delivered an invisible border in Ireland could only be ultimately abritrated by the European Court of Justice as it has sole rights of adjudication on EU law and whether customs and regulatory compliance rules could be waived at the border.

Secondly, in the EU’s eyes, as we have seen, the whole question of Britain exiting from the backstop is determined not by the very fact of a free trade deal, but what’s in it.

Again, we’re back at the fundamental dilemma. As the world’s fifth biggest economy, Britain is struggling to reconcile the need for high alignment (to protect the Irish border), with the desire for freedom to negotiate its own trade deals around the world.

Yet, so far the EU has resisted the idea that there can be two regulatory spheres side by side that are similar but not identical, with an ambiguous degree of monitoring, compliance and enforcement.

A fundamental red line for Brussels has been that it maintains "regulatory autonomy", i.e. it makes its own rules for its own internal market.

But London continues to challenge this on the basis that the UK is too big an economy to be subservient to the EU’s regulatory orbit.

The UK and the EU should be able to set "a totally new gold standard on how you do international regulatory cooperation," according to one official.

Theresa May at the famous Chequers cabinet meeting

Chequers provide the basis for this, is the argument, with its sector-by-sector alignment ideas. Even then Britain is already subject to being a rule-taker in a significant number of areas.

The proposal comes with the slightest hint of threat. "You want Europe to remain a global leader in regulatory standards," says the official. "But the EU would want to avoid the UK being too tempted to go the way of the US [in terms of regulatory standards], and so you have to find a way to do that which takes account of the political realities."

Theresa May’s strategy will involve a parallel line of pressure on Dublin.

All of these complex arguments about alignment and regulatory orbits should not get in the way of a continuing and fundamental determination to avoid a hard border at all costs.

This should be taken up bilaterally by Dublin and London. Expect phrases in the coming days reflecting both countries’ "common endeavour" to preserve the Good Friday Agreement.

"Ultimately, we need to find a way through this that Dublin feels comfortable with," says a source. "We have to try and disentangle the longer term commitment to no hard border, and this particular set of arrangements."

Dublin so far has resisted the "bilateralisation" of the backstop issue. It is for the EU27 to decide is Ireland’s line.

British sources admit that both parallel tracks as a way out of the impasse are complex, and would not command the support of parts of the ERG, not least because it exhumes Chequers.

But amid the fog of where we go next, this seems to be the plan.