Extending the time available to make a decision does not increase the range of Brexit options, but it allows for a more honest account of those choices and perhaps a more deliberative, less aggressively partisan evaluation of their merits. The real opportunity represented by the EU’s deferral of the UK’s departure date is to reset the way in which Brexit is debated, not just the object of debate.

That begins with acknowledgment that the answers are not delineated along party lines. There is a spectrum of possible relationships that Britain can have with the EU involving variable degrees of integration with existing institutions. The range is familiar enough: a customs union, the single market, the EEA, Efta and some combination, including full membership. The process of indicative voting in parliament has demonstrated the absence of either a Labour or a Tory consensus on the optimal position on that spectrum.

The government has failed to win support for Theresa May’s deal. She and Jeremy Corbyn have failed to arrive at a compromise. In such an impasse the case for putting Brexit to another public vote gets ever more compelling. But a referendum in itself is not a solution if there is no clear proposition on which the public could form a judgment. A flaw in the 2016 poll was the nebulousness of the leave option on the ballot paper. Brexiters deferred hard questions about what leaving meant in practice until after their victory. Those questions are still not sufficiently debated or understood.

This is where the prospect of a citizens’ assembly, supported by a handful of MPs and previously advocated by this newspaper, looks increasingly attractive. There are various models available, but the broad principle is that members of the public, selected to be representative of the country as a whole, take evidence on an issue and arrive at recommendations. The citizens themselves can have control over the process, including the vital decisions over who is invited to share expertise and give testimony. It is a deliberative mechanism with a proven record of finding common ground in polarised debates and nurturing civil engagement on matters that often provoke discord. A citizens’ assembly was instrumental in drawing poison out the debate ahead of Ireland’s 2017 referendum on revising abortion law.

With a modest application of political will, a similar process could be used to alight on a Brexit route within the six-month article 50 extension agreed in Brussels on Wednesday night.

There are two main obstacles. First, some MPs resent what they see as a usurpation of their own deliberative role. Second, Brexiters see the idea as a ruse by remainers to advance their side of the argument. The problem of parliamentary pride can be overcome by giving MPs ownership of the process. The assembly’s conclusions would be fed back to the Commons, which would retain its unique legislative privileges. As for buy-in among Brexiters, they should have confidence in the strength of their arguments. The evidence shows that a well-organised citizens’ assembly quickly proves its independence from those who advocated its formation. That is the beauty of them. They quickly earn their own legitimacy. It doesn’t matter if remainers want one more than leavers – there is no predetermined conclusion. All that is required is trust in a selection of British people to be fair-minded in consideration of evidence. The judiciary uses the same principle in courts every day.

The core objection to a citizens’ assembly on an issue of great national importance is that it is unfamiliar – not an established mechanism in British politics. But that is also its greatest recommendation. The normal procedures have failed. The political wheels are spinning on the spot without traction. Instead of revving the engines of rage and frustration ever louder, it makes sense to try changing gear – to shift the debate to new terms, in a new forum with a unique mandate. MPs fear that outsourcing Brexit deliberation to a citizens’ assembly drains authority from parliament. The opposite its true. The Commons would regain lost esteem in the public eye by demonstrating the willingness and imagination to innovate its way out of the current crisis.