Brexit came close to unravelling amid misunderstanding, confusion and farce this month. David Davis’s ordeal before the Commons Brexit select committee, with embarrassment over the stalling divorce negotiations and Irish border, captured the mood.

But the Prime Minister has managed to get through to the second stage of talks, which will focus on a trade agreement between the UK and the EU. In other words, the hard part.

Next week, Parliament will debate the Liberal Democrats’ amendment to the EU withdrawal bill. This calls for the public to have a vote on any Brexit deal, with an option of an “Exit from Brexit” if they don’t like what the Conservatives secure.

And this month’s problems casts doubt on the Conservatives’ ability to secure a palatable deal.

In that Brexit committee, Davis made two big admissions. The first: that the 58 sectoral Brexit “assessments” weren’t assessments at all. Those who have seen them – under a procedure rivalling access to the Crown Jewels – say they are descriptions of the sectors, not assessments of impact, and contain nothing unavailable on Wikipedia.

The second, more serious, point was that the decision to leave the customs union was taken by the Cabinet without any quantitative assessment of impact.

This doesn’t surprise me. Whenever I try to engage Brexiteers with technical issues which face supply chain industries, whose components cross borders, along with practical problems surrounding border certification and rules of origin, eyes glaze over.

Austrian prime minister Christian Kern: Brexit should be reversed

I suspect Brexiteers still don’t grasp how a customs union works for countries inside the customs union but outside the EU (like Turkey), and the barriers created for those outside.

It is now clear that problems like the Irish border stem from a decision shortly after the referendum to take Britain out of both the single market and customs union. We could have had a Brexit which keeps us in the single market (like Norway) or the customs union (like Turkey and smaller territories like the Channel Islands which are seeking to avoid trade friction). But the Government, under pressure from Brexit hardliners, chose not to compromise.

The result? The island of Ireland will see a divergence in regulation and products standard which will inevitably flow from departure from the single market; the necessity for border checks to stop unregulated migration from the Republic into the North; and the need for checks to ensure cross-border goods traffic pays UK rather than EU duties (a serious problem for mixed cargoes).

All this is hard to reconcile with the formal conditions of the Good Friday Agreement and with the political imperative for any Irish government – supported by the rest of the EU – to demonstrate that there is no hard border.

Minsters understood this imperative and agreed to avoid regulatory “divergence”. But, foolishly, they didn’t square it with the DUP. It is a constitutional outrage that a party with 1 per cent of the vote in the UK and unrepresentative of the Remain majority in the North should be the Ulster tail wagging the British dog.

But the DUP can reasonably claim that its position was clear from the outset; as was the Irish government’s and the European Commission’s. To have a negotiated compromise disowned at the last minute reveals serious incompetence on the UK side. But it all stems from the political constraints imposed by the hard-Brexit route chosen by the Conservative Government (and supported, lest we forget, by Labour). The first stage deal reached by the Prime Minister simply kicks the Irish border issue into the long grass.

The Davis admissions, on top of the Conservatives’ embarrassing failure to square their DUP partners over the future of the Irish border, comes as public opinion is turning.

A Survation poll shows that one in two voters now back the Liberal Democrat policy of a referendum on the deal the Conservatives finally obtain. That is a 16-point lead on those who are against giving the people having a say on the final deal.

Brexit bonhomie as May finally seals agreement with EU leaders Show all 10 1 /10 Brexit bonhomie as May finally seals agreement with EU leaders Brexit bonhomie as May finally seals agreement with EU leaders Britain's Prime Minister Theresa May is welcomed by European Commission President Jean-Claude Juncker Reuters Brexit bonhomie as May finally seals agreement with EU leaders EU President Jean-Claude Juncker greeting Theresa May at the EU Commission in Brussels PA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Prime Minister Theresa May poses for a picture with European Council President Donald Tusk REUTERS Brexit bonhomie as May finally seals agreement with EU leaders EU Commission President Jean-Claude Juncker walks behind British Prime Minister Theresa May EPA Brexit bonhomie as May finally seals agreement with EU leaders British Prime Minister Theresa May (L) and European Commission President Jean-Claude Juncker address a press conference at the European Commission in Brussels AFP/Getty Images Brexit bonhomie as May finally seals agreement with EU leaders British Prime Minister Theresa May speaks at a press conference with EU Commission President Jean-Claude Juncker EPA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Secretary of State for Exiting the European Union, David Davis (L) and Michel Barnier (2-L), the European Chief Negotiator of the Task Force for the Preparation and Conduct of the Negotiations with the United Kingdom under Article 50 enter the room by the emergency exit to attend British Prime Minister Theresa May press briefing on Brexit Negotiations in Brussels. EPA Brexit bonhomie as May finally seals agreement with EU leaders Britain's Secretary of State for Exiting the European Union David Davis (L), Britain's Prime Minister Theresa May (2-L), European Commission President Jean-Claude Juncker (2-R) and European Union's chief Brexit negotiator Michel Barnier (R) in a meeting on Friday morning AFP/Getty Images Brexit bonhomie as May finally seals agreement with EU leaders European Union chief Brexit negotiator Michel Barnier speaks during a media conference at EU headquarters Brexit bonhomie as May finally seals agreement with EU leaders European Council President Donald Tusk addresses a media conference at the Europa building in Brussels AP

For months, Brexiteers have told us that most people, even Remainers, simply want to get on with leaving. As recently as the general election, they were probably right.

The public has, however, become increasingly disenchanted by the Conservatives’ strategic, tactical and presentational incompetence in these negotiations. Their lack of a coherent plan has undermined a reputation for adept international diplomacy that took centuries to build.

A year into preliminary talks, the EU has essentially got what it wanted in terms of citizens’ rights and secured a hefty divorce settlement of £40bn-50bn. There is, as yet, nothing to show for British efforts.

Momentum is now behind a referendum and support will grow on the back of more weeks like this. I’ve said in the past there was a 20 to 25 per cent chance that Brexit won’t happen. I am optimistic that the odds are now moving further in our favour.

It will be a long process to get to the point when the Government concedes a referendum must happen. Eventually, though, a poll to get them out of a mess of their creation – an Exit from Botched Brexit – could prove too tempting to ignore.