The Brexit process is now a kind of wind erosion. The savage binary forces of British politics have collided with the unmoving position of the EU, and over time the wishful thinking in Westminster has been eroded down to a cluster of irregular geological forms.

Following Tuesday night’s thumping defeat, Theresa May glared at the landscape with a dazed look. "It is clear that the House does not support this deal," she told the Commons after the biggest defeat in parliamentary history. "But tonight’s vote tells us nothing about what it does support."

Theresa May has been forced to reach across the house but already she appears to be sticking to her lines. She needs Labour support to get the treaty over the line by 29 March, but the things that Labour wants – a permanent customs union, a second referendum, and even the banishment of No Deal – she has so far dismissed.

Tuesday’s defeat may have been seismic and the cosmos shaken, but the dynamic between the no deal, second referendum, Norway plus, or permanent customs union brigades has barely shifted.

Theresa May in the House of Commons on Tuesday

The only movement appears to be the prospect of an extension of Article 50.

"Let’s take a step back," says one EU diplomat. "We have to realise first, the ball is in the UK’s court. We eagarly await more guidance from the other side, and that will feed into any discussion about an extension. Time is short. We need a very clear view of the way forward, and a clear view of the process."

The week had begun with the letter of reassurance on the Irish backstop from Donald Tusk and Jean-Claude Juncker, designed to help Theresa May win the meaningful vote (or at least not lose it heavily).

Rarely can an exercise in diplomacy have had such little impact.

In fact, the tick-tacking between London and Brussels from early in the New Year went further than what EU 27 leaders had promised during the summit back in December.

Back then Theresa May had sought a two step approach: political clarification in December, followed by a legally-binding Joint Interpretative Statement in January.

EU leaders rejected legal reassurances or indeed any further clarifications at all (the summit conclusions in December made no reference to any follow up).

Nonetheless, from early January Theresa May’s chief negotiator Olly Robbins made several trips to Brussels, where his interlocutor on the European Commission side was the Secretary-General Martin Selmayr, who has taken the political lead now that the actual treaty negotiations are done.

On the European Council side most of the work was done by Piotr Serafin, Donald Tusk’s head of cabinet, and Jeppe Tranholm-Mikkelsen, the Council Secretary-General.

The talks were relatively low key. Irish officials were relaxed about the process, as there appeared no danger of the backstop being tinkered with.

The personalities – Robbins, Selmayr, Tranholm-Mikkelsen – were "a combination of people who have worked together for a long time now," according to one well-placed source. "None is particularly abrasive."

The thrust of May’s approach, therefore, was not to push once again for an expiry date to the backstop, or even "legally-binding" assurances on what "temporary" meant.

Rather it was to enhance a guarantee that the future trade relationship would be in place as soon as possible, so that the backstop would not need to take effect.

Underlying this approach was the amendment by the former Northern Ireland Office minister Sir Hugo Swire, tabled on 6 December in an effort to push the DUP into supporting the initial vote on 11 December, before it was pulled.

The amendment said the government would have to report to parliament in March 2020 as to how the free trade agreement was progressing and when it could supersede the backstop.

Parliament would also have to give its consent for the government to either extend the transition period by one year (from the end of December 2020), or enter the backstop.

The government would also be obliged to ensure that, if the backstop did take effect, it could only last for one year.

Downing Street was attracted to the idea. However, Mrs May realised that the EU would never accept a parliamentary veto over when the backstop began and ended.

So at December’s summit she instead focused on the timing of the trade deal.

Remember, Article 2 of the treaty states that "the [EU] and the United Kingdom shall use their best endeavours to conclude, by 31 December 2020, a [free trade] agreement which supersedes this Protocol in whole or in part."

While the "best endeavours" promise of December 2020, May wanted EU leaders to commit to something stronger. She wanted "absolute determination" that the trade deal would be in place by the end of 2021 at the latest.

In that situation the transition period could be extended by a year from the end of December 2020, again as provided for in the Withdrawal Agreement, or the backstop would kick in.

But if both sides were now committed to a new concept that was stronger than "best endeavours", ie "absolute determination", then surely the backstop would only have to last for a year, maximum.

"You’re not saying that if you’re in the backstop you will leave it in one year," says one source. "Nor are you saying this backstop will self-destruct after a year. It was an attempt to turn it into a positive, through the ‘absolute determination’ approach."

May had actually wanted the "absolute determination" phrase to be inserted into a Joint Interpretative Statement in January.

This was rejected by Brussels. It was not just because Ireland and other member states were allergic to the idea of anything legally-binding being tacked on to the Withdrawal Agreement, but because what mattered was not just dates and timelines, but the quality and texture of that free trade agreement.

"The leaders were saying in part," says the source, "that the best way of avoiding falling into the backstop, or if we do fall into it and want to exit quickly, is to have a plan. Not a sort of empty date that you can’t back up. So, let’s work on a plan on what the shape and content of free trade agreement will be."

Despite this setback, work on a joint exchange of letters between Theresa May and Donald Tusk and Jean-Claude Juncker continued right up until Sunday night, 13 January.

In her letter, Theresa May said there was a suspicion in Westminster that the EU would "not handle the negotiation of future relationship energetically or ambitiously". EU could even "down tools altogether and leave the UK permanently in the backstop arrangements."

This, she wrote, amounted to an "imbalance". The Withdrawal Agreement, and hence the backstop, was legally binding. The Political Declaration, setting out the future trade relationship, was not.

However, her letter fell short of asking for a further "legal commitment". She had also abandoned the "absolute determination" route.

Instead, Mrs May asked for a promise that the preparatory talks on the trade negotiations could begin as soon as the treaty was signed (ie, before the UK formally leaves), that "particular urgency" be given to finding a technological solution to the Irish border, and that the EU confirm a "legal connection" between the Withdrawal Agreement and the Political Declaration.

She also asked that, even if the trade negotiations were technically concluded, but had not yet been ratified by all 28 parliaments, then parts of that agreement could be "provisionally" applied, "rather than default to the backstop".

If the EU agreed these extra commitments, she wrote, "I am confident we shall never have to use the backstop."

Brussels was dismayed.

The anything-but-the-backstop approach was fine. But it had to be balanced by a positive outline of what there would be in the future trade relationship that would avoid a hard border in Ireland.

"If the UK came out and said, we’re going to pursue this and that avenue, or that this and that will plausibly and credibly provide the effect of not having a hard border, or not having the backstop, then that would be something," says a source close to the talks. "But this letter doesn’t deliver."

British sources take a different view.

The approach by Theresa May was, in their view, an incredibly difficult balancing act. The British side was upfront in that it was not pursuing the more outlandish demands that were emanating from the House of Commons about dumping the backstop. The most offensive aspects of it, however, needed "rebalancing".

Did May achieve anything?

Tusk and Juncker replied that "we are not in a position to agree to anything that changes or is inconsistent with the Withdrawal Agreement."

However, they did meet some of Mrs May’s requests. Preparations for the trade negotiations could, indeed, start as soon as the ink was dry on the signatures.

Parts of the trade deal could be applied provisionally, even before it was fully ratified by all 28 member states. However, the letter did not make any reference to the backstop in this context, simply that such a move was "in line with the legal frameworks that apply and existing practice."

The letter acknowledged, not so much a "legal" link between the Withdrawal Agreement and the Political Declaration, but that they were "part of the same negotiated package," and as such would be published alongside each other in the EU’s official journal.

London did take comfort elsewhere. Sources believed reassurances that were taken out of the December summit conclusions had found their way back in. Also, the EU now appeared to be explicitly acknowledging the UK’s ability to involve Stormont in managing elements of the backstop.

What did this involve?

On January 9, the British government published its Commitments to Northern Ireland and its Integral Place in the United Kingdom, what appeared to be a further, desperate attempt to get the DUP on board.

The government, the paper said, was "committed to a strong role for the Northern Ireland Assembly before the backstop could ever be brought into force," including a "mandatory consultation" at the point of choosing between the backstop and extending the transition if the free trade deal was not in place by the end of 2020.

The Assembly could debate and then vote on the issue, and the outcome would be put before the House of Commons, "placing clear obligations on the

UK Government and guaranteeing a strong voice for Northern Ireland."

If this was simply about whether or not the House of Commons could choose between the backstop or extending the transition period by a year, then that would be one thing.

However, any notion that Stormont held a proxy veto either on the application or duration of the backstop, was another, and would clearly not be a runner for the EU.

The paper made another promise. The Irish Protocol may have provided for alignment with "a small fraction" of EU Single Market rules in Northern Ireland, it said. However, while existing EU regulations or directives that were being updated or amended would automatically apply under a backstop scenario, if there were any new EU laws that fell under the scope of the backstop, then the EU "could not mandate the UK to accept that such a regulation must apply in Northern Ireland."

This raised eyebrows in Dublin.

Officials knew that London was going to set out a new set of promises on the backstop to try to reassure the DUP, but when the British paper arrived in Dublin, it was very late in the day.

Officials immediately noticed the promise a kind of Northern Ireland Assembly "lock".

"This idea," remarked one source, "that if there were any new EU laws in the future that would need to be aligned in Northern Ireland to avoid a hard border, that the Assembly would somehow have the capacity to disagree with aligning itself with that law. It certainly went to the edge of what is allowable under the Protocol."

Officials checked Article 15(5) of the Withdrawal Agreement which does, indeed, spell out that if the EU is bringing in a completely new regulation, there would have to be a discussion within the Joint Committee. This is set up under treaty and will comprise EU and UK officials.

The committee would have to discuss why such a regulation was necessary to comply with the obligation of avoiding a hard border.

If the UK objected, then both sides would have to look for other ways to achieve the same outcome. In the Tusk Juncker letter, the EU made it clear that it was up to the UK as to how they managed their side of that process, and so if it meant consulting with Stormont, then that was not a problem.

But if there was no agreement on an alternative within a reasonable period of time, in an extreme situation the EU could "take appropriate remedial measures" to ensure that the regulation was applied in Northern Ireland.

Nonetheless, London welcomed the clarification. "If it’s a totally new directive, then Stormont gets a lock on whether that applies," says one source. "We hand that veto over to Stormont."

Whether the clarification goes that far is a matter of debate. The point for London is that unionists fear the backstop gives the EU a "blank cheque" to introduce new laws into Northern Ireland over which local politicians have no say. "This is trying to rebalance it," says the source.

Despite all Olly Robbins’ efforts, the DUP instantly rejected all three gambits: the British government’s paper addressed directly to Northern Ireland, Theresa May’s letter to Tusk and Juncker, and Tusk and Juncker’s reply.

But come Tuesday night, and the announcement that the Withdrawal Agreement had been beaten by 230 votes, it was clear to diplomats in Brussels that the backstop was not the only problem.

"It’s not the backstop as such," says one senior official closely involved, "but a much deeper issue with what kind of relationship they want to have with the EU. Do they want to have a clean break? Do they want to remain, or to stay as close as possible? Closer than has been envisaged until now?"

Indeed, EU officials now viewed the backstop as something more akin to a metaphor for the whole dilemma. "It reflects all the contradictions in the UK position, and they are now coming to the fore. It is a much more fundamental question about what kind of position parliament can coalesce around."

The size of the defeat paradoxically took the heat off Dublin. But there’s no doubt that a narrower margin could have made life uncomfortable for the Irish government

Another EU diplomat put it thus: "I don’t see any pressure coming on Ireland in the coming weeks. Not for the moment. Of course, the backstop is a problem… But the defeat was so large, it would have been much worse for Dublin if Mrs May had lost by a narrower margin, by 40 or 50 votes. Then she could have said, I need concessions. But with [a defeat of] 230 votes it’s a bit more difficult. Of course, it’s part of the analysis. But we have stuck very closely to the solidarity principle.

"What people in the UK lose in their analysis is that this is not a classical EU negotiation. This is a different ballgame. OK, you’re big, you’re important – nobody denies that. But you’re leaving. That means that member states like Ireland have a privileged position."

In the aftermath of the vote, France and Germany sought a formal meeting of EU ambassadors to address the question of a possible extension of Article 50. The Romanian Presidency was reluctant to go that far, so an informal meeting was called instead.

In fact, at the prompting of Martin Selmayr, officials from both the European Commission, and then the European Council, under the guidance of Jeppe Tranholm-Mikkelsen, have already been meeting informally, road-testing the legal implications of a request from London.

"The reflection has started," confirmed a senior EU official. "Even if nothing is requested we have to prepare our legal thinking. We need to know in what kind of legal framework we’re operating."

That will be critical. At the end of May the European Elections take place, and the new parliament will be formally constituted on 2 July. So, an extension up to 1 July would be a safe option. But beyond that, according to several sources, there could be legal problems. So long as the UK remains a member state the EU treaties safeguard its right, and the right of its citizens, to be represented.

"After 2 July anything that the new parliament did without UK delegates would very likely be illegal," says one source.

Another senior official close to the Brexit talks adds: "If there’s an extension it would have to happen before 1 July, otherwise the UK would have to hold a [European Parliament] election, which would be a bit of a strange thing to be doing."

It’s understood that officials have considered making any longer extension conditional on the UK taking part in European Parliament elections – even if they were held separately, say, in September.

This is partly political. Any signal that the EU were reluctant to let British candidates take to the campaign trail would be jumped on by UKIP, who would seek to capitalise if and when British participation was eventually approved.

But an extension in itself is treacherous for political reasons, not least because there could be the bizarre scenario of the UK holding Euro elections while at the same time preparing for a second referendum or a general election.

"The last thing we need," says one official, "is the importation of the Brexit problematique into our own elections. If the Brits had still not left, three years after they had voted to leave, you can imagine the campaign of Marine Le Pen and others, shouting that Brussels has confiscated the people, and stopped the Brits from leaving.

"The elections are already complex on many different levels, so this is not an ingredient we want added to the soup."

Despite this, the debate is ongoing. The Financial Times has quoted a leaked Parliament legal opinion which states: "The possibility for the European Parliament to be validly constituted following the 2019 elections would not be affected by a potential failure by the UK to organise elections."

But the growing consensus in Brussels is that an extension request would be viewed favourably, so long as it was to facilitate a clear plan that was somehow bolted together using bits and pieces from the floor of the Westminster workshop.

As we have seen, however, the signs so far are not uplifting.

Theresa May spent Thursday meeting high profile Leavers, while delegating her subordinates to meet Remainers. At the time of writing Jeremy Corbyn was still refusing to meet the prime minister until she took No Deal off the table.

Two big ideas – a Labour-supported permanent customs union and the Conservative MP Nick Boles’ idea of a bill forcing the government to abandon No Deal – would split the Tories assunder, alienating both those for whom the only economic rationale for Brexit is an independent trade policy, precluded by a customs union, and those who are relaxed about, or even avid for, leaving with No Deal.

Other options like Norway Plus, in which the UK stays in the single market and customs union for a period of time, or a second referendum, will hardly be agreed by a Conservative leader who, despite the notion of the House of Commons taking control, still enjoys the government prerogative.

"Our interlocutor is the UK government," says one EU diplomat ruefully. "We’re not negotiating with the Parliament."

Theresa May’s prevarication on truly embracing opposition ideas is either a negotiating tactic, or a case of running down the clock so that enough of her own backbenchers, and Leave-supporting Labour MPs, will capitulate when confronted in March with the stark options of her deal and No Deal.

"The prime minister was humiliated in the Commons," according to a paper by Professor Anand Menon for the think-tank UK in a Changing Europe, "yet arguably more significant was the fact that the vote, finally, marked the moment when the House of Commons began what promises to be rather lengthy and ill-tempered process of elimination. Her deal is on life support and not looking well at all. But it is still too soon to say, definitively, that it is dead?"