Labour, the movement that prizes members’ democracy above all else, is now strongly in favour of a people’s vote on Brexit: that is the collective decision hovering over the party’s annual conference in Liverpool, and it speaks well of the wisdom of the Labour crowd.

According to a new YouGov poll, 86% of party members want a say on Britain’s future relationship with the EU, and 90% of them would vote remain in such a referendum. Though Labour undoubtedly captured many formerly Ukip votes in last year’s general election by promising to implement the result of the original 2016 vote, its rank and file now supports a second vote on Brexit. And this is by a margin of 24 percentage points greater than they gave Jeremy Corbyn in his contest against Owen Smith two years ago.

Conference at a glance: Labour nears consensus on Brexit Read more

The balance of opinion in Liverpool is clear. The question, of course, is whether members will get the chance to vote unambiguously on the matter on the conference floor. Tom Watson, Labour’s deputy leader, told the Observer: “If the people’s party decide they want the people to have a final say on the deal, we have to respect the view of our members and we will go out and argue for it.” Corbyn was more cautious on the BBC’s Andrew Marr Show, declaring – not unreasonably – that he would prefer a general election: “Let’s see what comes out of conference. Obviously I’m bound by the democracy of our party.” Doesn’t exactly quicken the pulse, does it?

All the same, Labour will leave Liverpool clearly committed to a people’s vote, formally or otherwise. In the short term, this will assist Theresa May, who needs all the help she can get (though when does she not?). Humiliated by her soon to be ex-EU partners in Salzburg, she must confront her cabinet colleagues on Monday , many of them convinced that the Chequers deal is indeed pushing up the daisies.

But at the Conservative conference in Birmingham, the prime minister and her remaining allies will say that Labour is playing reckless partisan games in the middle of a diplomatic process of great moment, reneging on its commitment to the 2016 referendum result, and proving that it is unfit for government. Indeed, that referendum defines the parameters and trajectory of her premiership: she became PM because a vacancy was created by its outcome. From the start, she characterised herself as the person who would implement that popular decision, by all and any means necessary. Even last year’s snap election – disastrous for her and the Tories – was driven by a desire to strengthen her negotiating mandate in Brussels with a decent majority in Westminster. The great gamble reflected the intensity of her wish to be recalled by posterity as the PM who successfully ushered Britain out of the EU, honouring the wishes of the voters.

Trust me, May is more likely to run through fields of wheat – her personal Studio 54, remember – wearing a “Vote Corbyn” T-shirt, singing the Internationale and smoking a reefer than she is to endorse a people’s vote. Her tribe will like it when she scoffs in Birmingham at the proponents of a final say on Brexit, just as they liked the wannabe-Thatcher firmness of her post-Salzburg statement in Downing Street on Friday. Expect to hear a lot about “finishing the job”, “holding our nerve” and “doing what is best for Britain”.

Rarely has conference season felt so introspective and confined. At precisely the moment that we should be raising our horizons as a nation and asking how to navigate these treacherous straits, the two main parties are looking inward and reverting to tribal type: fragmented, bickering, scoring cheap points when history is screaming that the time has come for bold thinking and statesmanship.

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So look ahead. Holding another referendum would indeed be a huge upheaval, suspending and dominating political life – yet again – for months. Under the terms of the Political Parties, Elections and Referendums Act 2000, the campaign itself would have to last at least 28 days – and that after the official campaign organisations on both sides had been designated. The Electoral Commission would need to endorse a question, which, it is already clear, would be a nightmare. Len McCluskey, the general secretary of Unite, Labour’s biggest financial backer, said on Sunday that the ballot paper should not include the option to stay in the EU. Confused? You will be.

Assume, though, that confronting such dilemmas becomes more attractive than maintaining our present course. Could a people’s vote get through parliament in the first place? Let us say, just for the sake of argument, that Labour (on a three-line whip), the Lib Dems, SNP, Plaid and Greens voted more or less en bloc for a final say. That gets you to 309. But deduct perhaps half a dozen pro-Brexit Labour MPs like Kate Hoey defying this putative whip. Back to 303. We now need to get to 320 (the notional majority is 326, but Sinn Féin does not take its seats and the Speaker and three deputies do not vote.)

It is true that 176 of the 317 Conservative MPs elected last year also backed remain in 2016. But it is a category error to assume that all of them would back a people’s vote in the Commons division. To date, only Anna Soubry, Sarah Wollaston, Justine Greening, Phillip Lee and Guto Bebb have given public support to a fresh referendum (other Tory MPs are certainly considering their options).

Would, say, 20 or more Conservatives break ranks and back a people’s vote? Quite possibly, and for one reason above all others: that the moment may soon be reached when to do otherwise would not only look unpatriotic, but (much worse for most politicians) utterly ridiculous. Only a few months ago, such an outcome would have seemed far-fetched. But the realm of the conceivable is expanding at hectic rate. Just watch. Ditch your preconceptions, and brace for impact.

• Matthew d’Ancona is a Guardian columnist