Leading members of the European Research Group, Jacob Rees-Mogg and former Brexit secretary David Davis, have publicly pledged their support to British PM Theresa May.

As MPs left Westminster on Thursday for a three-week recess to attend their party conferences, Theresa May’s allies had an unexpected spring in their step. The prime minister’s Brexiteer critics in the European Research Group (ERG) were looking foolish after their leaders distanced themselves from a few dozen members who publicly plotted against May on Tuesday night.

The ERG’s image as a highly disciplined machine had already taken a hit when it cancelled plans to publish its own blueprint for Brexit amid disagreements over its contents. Some members had apparently suggested including proposals for a missile defence shield and for a rapid response expeditionary force to protect the Falkland islands.

The ERG went ahead on Wednesday with the publication of a paper on the Border, launching it in the splendid library of the Royal United Services Institute on Whitehall. The paper had been eagerly anticipated amid a swirl of rumours that the ERG was preparing to back a bold move to resolve the dispute between London and Brussels over the Border backstop.

When the Commons Brexit committee, including ERG chairman Jacob Rees-Mogg, visited Brussels last week Michel Barnier told them how he wanted to “de-dramatise” the backstop.

“We need the necessary controls but we don’t want in any way to undermine the constitutional structure of the United Kingdom. We need to look at the individual controls that are necessary,” he told the MPs.

“We need to see how and when and where these controls would take place. They could be dispersed. They could take place in different places, on board vessels, in ports outside Ireland. They could be done using technological means.”

“So @10DowningStreet is now actively impeding the EU in trying to find a solution to the Northern Ireland border problem in order to unlock a #CanadaPlus FTA? Unbelievable.”

Instead of embracing the de-dramatised backstop, however, the ERG’s Brexiteers lost their nerve and produced a paper full of warmed-up proposals for technological and administrative fixes for the Border.

Jackson fell in dutifully behind the ERG’s new party line, tweeting that “with political commitment and technical solutions this paper can unlock the negotiations and the real prospect of a Canada Plus whilst respecting EU red lines and GFA [Good Friday Agreement]”.

Downing Street was taken by surprise by the ERG’s loss of nerve, revealing that if May had been asked about the paper during prime minister’s questions, she would have said that “we don’t believe that the answer is to move the Border” – something the ERG did not, in the end, suggest.

A few hours later, a senior cabinet minister told me the government was united in its opposition to the EU’s version of the backstop, even in its de-dramatised form.

“This is not just the DUP, it’s the Conservative Party, Remainers as well as Brexiteers. We can’t have Northern Ireland in a separate customs territory to the rest of the United Kingdom,” he said.

No alternative provided British negotiators have yet to propose an alternative to the EU’s backstop text in the draft withdrawal agreement and they have been dragging their feet about providing Barnier with information about trade flows and current checks between Northern Ireland and Great Britain.

The Conservatives may be committed to what May likes to call “our precious union” but the unresolved issue of the Border serves another purpose in the negotiations. It remains a strong argument against the Canada-style free trade agreement favoured by the Brexiteers and could serve as a lever to persuade the EU to bend their rules on the single market and customs union to Britain’s advantage.

British ministers believe that if Dublin doesn’t blink when confronted with the cost of a no-deal Brexit to Ireland, the other EU member states may agree to move final resolution of the Border issue from the withdrawal agreement into the negotiation of the future relationship. If it is still unresolved after Britain leaves the EU next March, the Border could become more useful still to Britain as it negotiates the terms of its future trading relationship with Europe.

The idea of “la perfide Albion” is deeply engrained in the European political consciousness, summed up brutally by Charles de Gaulle in his memoirs:

“Pour l’Angleterre ... il n’y a pas d’alliance qui tienne, ni de traité qui vaille, ni le vérité qui compte.” (For England, there is no alliance that holds, no treaty which is respected, no truth which matters.)