Chancellors ought to be able to count, so I was a bit concerned to hear Philip Hammond say: “No one wants to fight the European elections. It feels like a pointless exercise.”

That’s two inaccuracies in two sentences. There are plenty of people who are mustard-keen to fight the European elections. They include Nigel Farage, who has just fired up his new Brexit party by telling everyone “it will be no more Mr Nice Guy”. Add your own joke here. At the other pole of the argument, Change UK will be hoping to make an anti-Brexit splash with its electoral debut.

Some are predicting that turnout for these elections will be poor, but I suspect there are plenty of voters who will see them as an exercise with lots of point. Leavers will have a means to express their anger that Britain is still in the EU. Remainers will have a way to voice their demand for another referendum. Voters who are simply cross that Westminster can’t resolve the Brexit nightmare will be able to express their fury at the ballot box.

What Mr Hammond was really saying is that no one in his party relishes contesting the European elections. Tories dread them and are right to do so. Even in normal circumstances, they would struggle because they have been in office for nine years and voters traditionally use midterm elections to give a kick in the ballots to the incumbents. Current circumstances are abnormal and not in a good way for the Tories. They will go into these elections as a party poisonously divided about the most important issue of the day under a leader who has said she is on her way out. More, Mrs May is a prime minister who is told to her face by Tory MPs that she ought to have removed herself from Number 10 already.

I do not envy whoever has to write the contents of the Conservative manifesto for these elections. Unless Mrs May has been pushed to a different position by the time they take place, we must assume that the manifesto will recommend her withdrawal agreement to the country. That deal is not only unloved by voters, it is detested by the large numbers of Tory members who are no-dealers. A Conservative election agent in the key battleground of the Midlands bleakly predicts: “Our people will simply not come out.” The fear for them is that Tory activists will go on strike and many Brexity Tory voters will protest either by staying at home or casting their votes for Ukip or the latest Farage vehicle. The Tories will likely suffer desertions on their other flank as well. There is a substantial electoral group in Britain that is often forgotten. These are the Tory Remainers, the millions of Conservative-leaning voters who wanted to stay in the EU back in 2016. At least some of them will be defecting to the anti-Brexit parties.

Our Opinium poll suggests that the Tories are heading for a marmalising so bad that it is without historical precedent. Among voters who say they are certain to participate in the elections, only 17% choose the Conservatives. This poll doesn’t claim to be a precise prediction of what will happen at the end of May, but it does point to a shockingly bad outcome for the Tories. This vote share is six points down on their previous record low in Euro elections, which was in 2014. The sage of electoral history, David Cowling, tells me that the Conservatives have never scored as badly as 17% in any UK-wide election from 1832 onwards. No wonder the Tories are desperate to avoid these elections. This they could do, but only by ensuring that Britain has exited the EU before polling day, a task that the government has repeatedly proved incapable of fulfilling.

One of the merits of these elections happening is that they might finally force clarity from Labour

Labour looks to be in better shape to contest these elections, but the 29% vote share indicated by Opinium is not exactly fantastic for a party aspiring to be the next government and Jeremy Corbyn has his own reasons to be nervous. For Euro elections confront the Labour leader with a choice that he has spent many months trying to avoid. Some of the party’s senior figures, notably Tom Watson, Emily Thornberry and Keir Starmer, have become increasingly vocal in saying that Labour must commit to a fresh referendum on Brexit, no ifs, no buts, no hesitations, deviations or obfuscations. Others on the top team want the party to carry on hiding in a thicket of ambiguities. One of the merits of these elections happening is that they might finally force clarity from Labour. The party will have to publish a manifesto and that prospectus will have to say whether or not Labour unequivocally supports another referendum.

The upper echelons of the party are preparing for a struggle over who controls the writing of the manifesto. Mr Corbyn’s team would like to put it in the hands of their friends on the national executive committee, which is dominated by supporters of the leader. That would cause outrage in the shadow cabinet. A senior figure on Labour’s frontbench says it will be “beyond unacceptable” if a manifesto is published that doesn’t have the approval of the shadow cabinet. Labour’s candidates for the European parliament are overwhelmingly anti-Brexit and they will have something to say if there is an attempt to impose an ambiguous position on them. Richard Corbett, the leader of Labour’s MEPs, warns that the party will “haemorrhage support” to pro-referendum parties if Labour is not committed to a second vote.

The divisions of the Tories and Labour present a great opportunity to challenger parties that are united around clear messages about Brexit. As I’ve remarked before, one of the unanticipated consequences of the past three years has been to create a highly motivated, articulate and energised pro-European base in British politics. You can now get a million people marching in London to proclaim their support for EU membership, a phenomenon never previously witnessed. It is even arguable that Britain now has the largest pro-EU movement in Europe. There’s an irony for you.

This is encouraging for all the parties that will use the Euro elections to campaign for a fresh referendum: the Lib Dems, the Greens and the Nationalist parties in Scotland and Wales. It also provides an excellent opportunity for Change UK, providing the electoral commission approves the application of the Independent Group to become a political party in time to meet the nomination deadline. They are currently working through a small mountain of applications to be Change UK candidates. Some are coming in from one nation pro-European Tories, including at least one former cabinet minister. Some are ex-Labour people. Other aspiring Change candidates are people with no previous affiliation. These include people in jobs in public service or the business world, which they will have to give up if they publicly declare a party allegiance. It is a measure of both the passions aroused by Brexit and despair with the big two parties that people are prepared to sacrifice good careers to stand for a party that does not yet officially exist in an election that is not guaranteed to take place.

There could not be a better electoral launchpad for Change UK than European elections. They have a straightforward message, popular with a lot of voters, that Brexit is a folly and must be put back to the people for a final verdict. Seats are contested in large regions and awarded by proportional representation, not first past the post, which maximises the chances of Change UK translating votes into representation. This is also true for the Lib Dems, the Greens and the Nationalists and means that it matters less if the anti-Brexit vote is spread among them.

There will be two principal no-deal Brexit parties on offer to the electorate: Ukip and the Brexit party. Between them, they will harvest votes from the substantial “let’s just get out” segment of the electorate. It will be by aggregating the votes of parties on the two sides of the argument that we will get a measure of which is the more popular position.

There’s a good chance the contest will turn into a kind of proxy referendum, though it won’t be a substitute for the real thing. Those hoping for that will want to see a strong collective performance by the parties that are pledged to delivering a people’s vote. Pace Philip Hammond, these elections will not be at all pointless. They will have a very sharp point and it will be aimed at the most sensitive areas of the government’s already raddled anatomy.

• Andrew Rawnsley is Chief Political Commentator of the Observer