I met a press photographer in Westminster on Sunday afternoon who was in a rush, hurrying, he told me, to file some pictures from the demonstration at which he had just been working.

Knowing there were two demonstrations on I asked him which he had been at - the pro-Brexit or anti-Brexit rally. 

"I’m not sure which it was," he said. "I just know they were all really, really angry". We couldn’t both help but laugh.

There are some moments of levity in British politics at the moment, although laughter is quickly followed by the knowledge that the events that unfold here this week affect everyone - from Westminster to Wexford.

British politics is currently long on anger and short on ways to remedy the rage. We thought that this week, Theresa May, the British Prime Minister who raised kicking a can down the road to an art form, would run out of road. Something had to give and it increasingly looked like it might be her leadership.

But Mrs May once again defied the odds, although not by reaching a détente between the many factions in her party who want different types of Brexit. She proved everyone wrong by finding another little bit of road.

Theresa May’s premiership is one that has been held in place by division.

An extreme difficulty uniting the many different views of what Brexit should be into one coherent policy, as well as no unified view as to who should take over from her were she to be pushed out, have meant that Mrs May remains at the helm of British politics in spite of every prediction that she could not make it this far.

This week was in some ways not about whether individuals are pro or anti-Brexit. This week was about implementation and those on both sides of Brexit are forced to agree that when it comes to that implementation, it is an unmitigated mess.

There is no clear majority for Mrs May's deal, no clear majority for no deal, no clear majority for a second referendum ... I could go on.

When you start a negotiation of any kind it is wise to think about what those on the other side of the negotiating table might want, what their restrictions might be, and the difficulties that may inform how far they can come to meet you. 

You should try to at least to walk in their shoes for a little while. You could call it strategy or tactics. Actually, you could just call it politics.  

Brexiteers believe that the EU is trying to trap them and keep them in a customs union through a Northern Irish backstop. It comes from a very deeply-held lack of trust in the EU institutions. For these politicians, an assurance from Brussels that the backstop is an insurance policy that no one wants to see coming into force is virtually worthless.

Brussels cannot be believed, they say. It’s striking that when you suggest any reciprocal lack of trust might be the reason a backstop is required, many of the same politicians are often clearly bemused and sometimes mildly offended.  

Theresa May tried to sell her Brexit plan initially as part of a tour of Northern Ireland, Scotland and Wales. Now, Mrs May is trying to salvage her deal with a tour of EU capitals. 

Few in Westminster believed her first tour would solve her problems. Almost no one believes this second tour can remedy the issues either.

The EU would need to make very substantive changes in order to assure Theresa May of victory in a Commons vote. 

Not only has the EU said this deal is the best it can offer, but any changes at this point would only seek to undermine the EU as a negotiating force in the future.

The questions in Westminster now revolve around when this vote might return to parliament, and whether Mrs May will have survived as Conservative Party leader long enough to see its return.

There has been much talk that the vote will not happen this side of Christmas, but as MPs mull over the strong chance of government defeat, many now think it might be better that the vote happens sooner rather than later.

It would, they argue, at least mean that alternatives could be looked at as a matter of urgency. Some think Mrs May might be running down the clock, waiting until close to the Brexit date to make MPs vote for her deal out of fear of the alternative.

It would certainly be a strategy, albeit an incredibly risky one. But the events of the last few days have made many question whether there is a strategy in play here at all. That has become the far bigger concern in trying to unpick the Gordian knot that is Brexit.