Those still fighting to keep the United Kingdom in the EU are doing themselves no favours. Despite Saturday’s protests for a second referendum and Commons manoeuvring, a significant portion of the public backs the UK’s vote to leave the EU – and democracy requires it to do so.

The terms of exit previously negotiated by Theresa May were rejected by remainers, but without any coherent strategy to push that rejection to a satisfactory conclusion. The new deal from Boris Johnson is worse, but even Magna Carta was not perfect. The deal available is serviceable for withdrawal on 31 October. It should be passed and the nation put out of its misery.

The concession might reverse one of Johnson’s many do-or-die pledges, but what is new in that?

On one condition. The terms of a new trading deal with Europe need not be an issue since they are up for negotiation during a transition period. Johnson played fast and loose in the deal’s political statement that supposedly governs this transition. He “hardened” it in a largely successful effort to win over his own right wing and obviate the Irish backstop. To that end he withdrew the references to a customs union and single market as they appeared in May’s abortive deal. But he conceded easement on regulatory alignments, EU nationals’ status and Labour’s demand for workers’ rights.

Johnson should now extend that easement to the proposed amendment that the upcoming negotiations include remaining in a (or the) customs union. Embracing that possibility would cut the Gordian knot of the Irish border at one stroke. It would dismantle Michael Gove’s ludicrous no-deal preparations. It would end the debilitating uncertainty surrounding trade with Europe. It would remove the economic sting from Brexit, while honouring its political objective of disengagement from “ever closer union”. The will of the British people would finally be met – in compromise terms that respected the size of the remain minority.

The sole cost to Johnson in such a concession would be Brexiters’ phantom trade deals with the rest of the world. Any detailed analysis shows such deals to be moonshine – chauvinist rhetoric never mentioned at the time of the referendum. The concession might reverse one of Johnson’s many do-or-die pledges, but what is new in that? It was only made to help Johnson beat Jeremy Hunt to the party leadership.

A customs union amendment conceded by Johnson should enable Labour to support the remainder of his withdrawal bill. Some “hard” leavers might defect, but it would be time for remainers to accept political reality. They would still have much to play for in the upcoming transition.

The spectacle of the House of Commons agreeing in such a fashion would reassure the EU. It would be greeted by the British public with a shout of relief audible the length and breadth of the land. It just needs Johnson to agree to the amendment: like Caesar back from Gaul, he could then claim his triumph.

• Simon Jenkins is a Guardian columnist