European elections take place on 23 May, almost certainly. For this great chance to summon the pro-EU, pro-referendum vote, give thanks from the bottom of our hearts to the unbelievably useful idiots of the European Research Group hard core. Special thanks to Mark Francois, idiot-in-chief, to Peter Bone, Steve Baker and all the other refuseniks, including our friends the doughty DUP.

Were it not for them we would by now have left the EU on time on 29 March. We would be on our way out of all EU political institutions, out of the common agriculture and fisheries policies, no freedom of movement but free to trade with the Faroe Islands. Ahead would lie a hard-Brexit prime minister forging the hardest trade policies. Reasonable Brexit voters will look back in anger at what these fruitcakes have rejected in pursuit of an impossible no-deal crash-out. Idiocy is just a polite word. But let’s give thanks for their pig-headed obstinacy. Long may it last.

Theresa May will do her best to bring them to their senses before 22 May, to avoid suffering the humiliation of European elections where the Tories may not even come fourth. These elections will reinforce what polls have shown for well over a year – a remain majority of some 8%. A good pro-EU result will make leaving without another vote look scandalously undemocratic. Can May persuade her ERG hold-outs in time? Though persuasion is the prime tool of a politician’s trade, it’s never been her forte: the ERG looks unlikely to succumb.

Both main parties are currently unhinged in their own particular way – though both have sages within who tear out their hair at the folly of their own side. The only good that may come from the Brexit trauma is to finish off a zombie two-party system that keeps sworn political enemies locked together in two electoral coffins. But the breakaway Independent Group will struggle when it confronts the democracy-killing bulldozer that is first-past-the-post.

These elections should see the pro-Europeans triumph. While Labour still prevaricates, the Liberal Democrats, Greens and Change UK (the Independent Group as was) are the only unequivocal singers of the EU ode to joy. They all campaign for proportional representation, yet seem to have failed in that spirit of cooperation and coalition. If, just for this one election, they combined as a single pro-EU, pro-referendum grouping, they would do far better. Not only would they win more seats and votes, they would shake Labour off the fence for fear of being eaten alive.

Of the 73 UK seats in the European parliament, the Greens have three and the Lib Dems have one. A party needs to reach a minimum threshold to have a chance of winning a seat – 10% in the south-east, 30% in the north-east. Martin Baxter of Electoral Calculus reckons that the three parties standing together would gain an extra six seats. But that’s just on the hard maths. Add in the optimistic politics of pooling energies into one loud voice, and they could gather shedloads more, electrifying Labour.

It hasn’t happened. The chance to register with the Electoral Commission as a joint entity for this election passed two weeks ago. The Lib Dems say they reached out to the other two to explore some cooperation, but were rebuffed. The Green party says it had “no plans to field joint ‘remain’ lists”, and with its “long and proud history in the European parliament” it is “a strong and unwavering voice for remain”. Change UK says it wants “no alliance and no pacts but to be a new party standing on its own”. So there you have it. The parties that want to break the mould and change the system just couldn’t get it together.

Still, at least they won’t waste their ammunition targeting one another: watching Nigel Farage and Gerard Batten take chunks out of each other as they narcissistically try to explain the small difference between their xenophobic Brexit parties will be an enjoyable spectacle.

What matters most now, in this traditionally no-show election, is getting out the vote. Everyone needs to register by 7 May. And to the 3 million EU citizens living here who may not know they have that right: it’s easy online. All students need to register (colleges used to sign them up until they were banned under David Cameron’s rules of individual registration, designed to knock out younger, poorer and more mobile voters).

Despite a rising population, registration has dropped by 400,000 in the last year. Now we have seen their climate campaigning, we can be reminded that 1.5 million 16- and 17-year-olds deserve the vote – think how MPs might shift their priorities on climate, school funding or university fees if they had to solicit votes from sixth-formers who could swing seats in marginals. It’s too late this time; there’s no chance under May since so few young people vote Tory, but it’s been Labour policy for a decade.

Westminster polls are bouncing on bungee ropes, but the Electoral Calculus poll of polls shows how hard the Tories are being battered by their failure to deliver Brexit on time. Yet the one constant, for over a year, has been the shift away from Brexit to remain – through death and coming of age, and from those who didn’t vote in the referendum and say they would vote remain now. The great question is whether there is enough campaigning firepower among the million marchers and the 6 million revoke petition signatories to get the vote out for the pro-European parties on 23 May.

And that will include Labour. Although politely dancing the steps of discussion with Theresa May, Keir Starmer’s presence at the table makes certain that there is no chance, absolutely zero, of any deal unless confirmed with a public vote.

• Polly Toynbee is a Guardian columnist

• This article was amended on 16 April 2019. The deadline for voters to register to vote in this year’s European parliament elections is 7 May, not 3 May as an earlier version said.