Just as the UK’s Conservative government hit new lows with its long-awaited deal to leave the European Union, Mr. Stop Brexit was scaling new peaks. Rain or shine, Steve Bray, bedecked in a Union Jack amalgamated with the European Union’s gold-star logo, stands outside the Houses of Parliament in London, interrupting live newscasts by yelling out “Stop Brexit!” or busting onto broadcasts with his “Stop Brexit!” placard. As Prime Minister Theresa May’s weak, divided government teetered through yet another Brexit-induced bout of political chaos days ago, Mr. Stop Brexit’s protest played out in a hilarious game of cat and mouse with a BBC editor, who kept shifting the frame of a live interview feed to crop out the campaigner, only for Bray to keep outpacing the camera switches.

For many Britons watching Mr. Stop Brexit—at least for the 48 percent who voted to remain in the European Union in 2016’s referendum—the reaction to his protests must be: if only. Brexit has jammed up British politics, consumed it—and broken it. May’s just-announced EU-withdrawal deal is so bad that everyone hates it, albeit for different reasons. British commentators are suggesting she must have a rabbit up her sleeve, because there is no other explanation for her insistence on going through a parliamentary vote on this lambasted deal, in full knowledge that swaths of her own party could help to crush it.

Nobody knows what will happen if this deal is defeated next week: government meltdown? a general election? another referendum? a national nervous breakdown? Politics has been so paralyzed by Brexit that it sometimes feels as though only a sense of British understatement, combined with a dogged determination to hang on to a reputation for orderliness, is keeping things from collapse. Few surmised this impossible situation better than British actor Danny Dyer who, in a scatological rant on a morning TV show a few months ago, described Brexit as a “mad riddle.”

In the face of such chaos, it is small wonder that Brexit-watchers are looking to the Labour opposition to save the day. Taking Britain out of the EU was a populist-right project—tethered to the far-right rampage running through Europe and allied to US President Donald Trump, who foretold his own election win as “Brexit plus plus plus.” Leavers ran a campaign motivated by free-market fundamentalism while animating a peculiarly English form of nativist nostalgia (essentially, a xenophobia-laced longing for Empire).

There are some left-wing Brexiters, and a handful of them are Labour MPs, though most of those MPs who back Brexit do so mostly because they represent Leave-heavy constituencies. But the left movement more broadly, including not only the Labour Party but also the unions and the grassroots, supports Remain (with the caveat that most probably also believe the EU does need reform). Still, a third of Labour voters, some in the party’s electorally critical heartlands in the midlands and north of the country, voted Leave. On top of which: Remain lost the 2016 vote. So how can Labour, with its focus on participatory politics intended to combat years of disillusion and exclusion, now proclaim that the one thing millions of people did actually bother to vote for is the thing the party now wants to ditch?

Set against that problem is the mounting evidence that the brighter future promised by Leave campaigners was a mirage. Theresa May, hamstrung by her own unnecessary red lines and undermined by the hard-Leave cohort in her own party, has negotiated a deal that is measurably worse than staying in the EU. Indeed, the government’s own reports show that every version of leaving the EU harms the UK economy; the differences are only ones of degree. Such damage will hit hardest exactly the section of the population least able to afford it.

Lately, when leading Leavers are asked why the UK is still pursuing Brexit, the answer is: because we voted to.

Labour—its fortunes recently revived after a leftward turn under democratic-socialist leader Jeremy Corbyn—has so far deployed an ambiguous formulation that held together its coalition of Leave and Remain voters, while holding the government’s Brexit negotiations to account. Now, with Parliament expected to forcefully reject May’s deal, precipitating what is described as a constitutional crisis, Labour is going to have to switch things up.

Currently, the party is pushing for a general election, arguing that if the Tories can’t deliver on such a key policy, they should step aside already. Labour routinely comes out ahead of the Conservatives in polling. More tellingly, there’s majority support for Labour’s economic program, which is premised on large infrastructure projects, local investment, public ownership of rail and utilities, investment in welfare, and higher taxes for the highest earners.

Public appetite for this ambitious economic restructuring is fueled by the hardship unleashed by the Conservatives’ austerity policies, now eight years in, and by the decades-long, ravaging effects of neoliberalism. Devastating cuts to public services and local authorities have driven large sectors of the population into decline and despair. When UN poverty envoy Philip Alston visited the UK weeks ago, he reported a horrifying level of poverty—14 million people are affected, a fifth of the population, with 4 million of them more than 50 percent below the poverty line, and almost half of all children are poor. Scathingly, he said that the British government was in denial over the misery inflicted by its own austerity policies. An academic study released this summer suggests that the areas hardest hit by austerity were most likely to have voted to leave the EU. For Labour, an election win would mean not just the chance to secure a better Brexit, but the chance to cauterize some of Brexit’s causes, drawing the poison of poverty and inequality (the worst in Europe) out of the political equation.

Labour’s claims that it could negotiate a better Brexit deal have some traction: The party isn’t fatally divided over Brexit like the Conservatives, lacks May’s obsession with driving down immigration figures, and is more flexible over bits of the EU relationship that are roadblocks for the current government. The EU would need to reopen negotiations that it currently insists are closed, but this would be hard to resist in the face of a freshly mandated UK government. Sources close to the Labour leadership suggest that, should an election be called, the party could campaign to renegotiate Brexit and then offer a referendum on the deal. (Some, though, worry that Labour’s mostly Remain grassroots and voters might not turn out for this position.)

The Brexit maelstrom makes anything possible, but it is still unlikely that Conservative MPs would vote to trigger a general election—why would turkeys vote for Christmas? Within the Labour movement, many are focused on building support for a second referendum, which the party grassroots overwhelmingly supports. For a campaign not backed by the leadership of either of the main political parties, the People’s Vote, as it’s called, has picked up considerable steam. Some 700,000 turned up to a People’s Vote rally in London in October. Meanwhile, polling, put together by the anti-racist group Hope not Hate and the independent pro-Remain Best for Britain campaign, shows support for a popular vote in every constituency in the country. This does not translate as support for Remain—some Leave areas now support a referendum, too. And there is a worrying gambler’s appetite for the most destructive Brexit of all: crashing out of the EU with no deal, which up to 30 percent of the public supports.

This same polling now shows a switch from Leave to Remain in 193 constituencies, with Labour voters accounting for most of the traffic. Labour’s Leave voters simply aren’t as fixated on the issue as Conservatives; for Labour’s Brexiters, the National Health Service, wages, and jobs are more important. The party also gained a chunk of young, first-time voters in the 2017 election who are Remainers; their loyalty—and that of Labour’s wider, generally pro-EU base—might be tested if Labour refuses to back a second referendum.

The People’s Vote campaign has mostly been backed by centrists—including some Labour politicians critical of Corbyn—and figures such as former Labour prime minister Tony Blair. This is a terrible look for the campaign, coming over as a continuity project at a time when the hunger is clearly for change. Were Labour to come out in support of a second referendum, the party would have to make clear that it is not supporting the status quo ante—this, after all, is precisely what many voted against in 2016. There would have to be a different offer: the promise of the party’s radical economic agenda, the delivery of which could be hastened by the referendum, since the Conservatives would surely not survive a popular vote that killed off its current main policy. By this analysis, Labour’s campaigning for a People’s Vote would bolster its grassroots electioneering game, while sweeping up needed voters: in Remain-heavy Scotland, and from disgruntled pro-EU Tories (voters in swing Tory seats back another referendum). This is why, as one Labour organizer puts it, the party “needs to go into a referendum campaign with some energy and leadership rather than being dragged into it backwards” by unfolding events.

For backers of both the Corbyn project and a People’s Vote, there is an added dimension: international socialism. Across Europe, center-left parties have collapsed while the far right is growing, with many leftists looking to the UK Labour Party for a model of progressive political revival based on grassroots organizing and a left economic platform. Labour could lead the fight against the far right across the continent—but this could be harder to do outside the EU. Meanwhile, critical issues such as climate change and corporate tax avoidance need transnational solutions, which are more readily available within a closer EU relationship.

But still, a popular vote has pitfalls. It’s a massive gamble, in a context where Leave voters seem to accept the reality that Brexit isn’t going so well and yet still want the government to get on with it. It’s true that there has been a national shift toward Remain, but it is not decisive. A campaign to stay inside the EU, even if it won over Labour Leavers, would still have to persuade the squeezed middle Conservatives who formed the rump of the Brexit vote. The first referendum was toxic and divisive; it is unclear how a second one could avoid being the same, only more so. And it’s likely that the pro-Brexit right wing will tap into a sense of Leave disgruntlement over being asked to vote again, funneling resentment in an increasingly populist right direction.

All of which means that a Labour “rescue” from the Brexit mess might be more about forcing the government to soften its withdrawal deal, thus limiting the damage. Any Brexit is predicted to slow growth, but so, too, are Conservative policies. As Labour shadow chancellor John McDonnell pointed out at the party’s annual conference in September, “The greater the mess we inherit, the more radical we have to be.” Whichever strategy is chosen, it may make sense for Labour to play out the parliamentary process sequentially, so that it is seen to be exhausting options, rather than closing them off.

Everyone wants easy fixes, from the Brexiters’ impossible cries of “Let’s just leave!” to the pro-EU insistence that a second vote will solve everything. But there is no simple way out of the Brexit mess; there are no good options, barely even least worst ones. A second vote on the referendum might not be the best option—but it could also end up being the only one available.