There are no good options for Labour on Brexit. Accepting this fact is both depressing and liberating. Being on the left is supposed to be about unbounded optimism, a belief that what is deemed politically impossible by the “sensible grownups” of politics can be realised, with sufficient imagination and determination. But recognising that there is no magic button that will end the Brexit debate is to be freed of the stress of searching for the impossible.

Supporters of every position on Brexit should be honest about the downsides of their chosen strategies. Labour’s priority is, rightly, a general election. When Theresa May declared from a Downing Street podium that she was seeking to dissolve parliament in April 2017, she wanted to make the election entirely about Brexit. Labour did not allow her to do so, shifting the conversation on to domestic issues, where it was strong, from hiking taxes on the rich to investing in public services to public ownership: issues that unite remainers and leavers. Even though voters have priorities other than Brexit, such as stagnating wages, housing and the NHS, repeating the 2017 strategy this time would be far more challenging, to put it mildly. Labour’s electoral coalition, which encompasses both pro-remain Kensington and pro-leave Ashfield – will be placed under severe strain. The fact that Brexit dominates political debate is bad for Labour because it suppresses its anti-establishment politics; its leading figures are left looking like triangulating politicians, the same as the all the rest.

Is this a good option? No. None of them are. But such a deal would solve the intractable Northern Ireland border problem

Then there’s a second referendum, which may yet happen. Labour will have to make the best of it if it does. Yet we have learned from the Scottish independence vote and with Brexit what referendums do to our politics. They foster bitter divisions in ways that parliamentary elections tend not to do. That is why they can be such uniquely fertile political territory for the populist and far right. A referendum campaign would in effect hand the most demagogic, reactionary elements of British life a megaphone for several months. There are those who say well, we are already bitterly divided – how much worse can it get? To put it gently, they lack imagination: a new vote will be far uglier than the last, and its advocates should at least devise a strategy to deal with that.

Although economic grievances were critical in delivering the referendum result, Brexit has fomented an all-out culture war. The most meaningful division in society is not between remainers and leavers, or young people and their grandparents, or even Labour or Tory voters. It is between a rapacious elite that has plunged Britain into economic and social crisis on one hand, and a majority that suffers the consequences on the other. The culture war distracts from this understanding of class politics, which underpins Labour’s mission. In a referendum, Labour will risk looking as if it supports the status quo. All the work it has done in leave-supporting constituencies, without which it cannot win an election, may be fatally undermined. The left was long berated for emphasising principles over power, for not understanding that without forming a government it cannot help people. Now it pursues an electoral strategy to win an election and deal with the injustices that caused Brexit, the same people denounce it for putting party ahead of country. A pro-Brexit slogan such as “Tell them again” will resonate and inflame passions. Polls show there is no decisive majority for remain – and that’s in the absence of an up-and-running leave campaign. Imagine if leave won again? The narrative would be that a remain elite had tried to subvert the result, dragged the nation through another vicious campaign, and must never be listened to again.

Another possibility is what has been labelled “common market 2.0”, or Norway plus. Britain would remain part of the single market and enter a permanent customs union. Is this a good option? No. None of them are. But such a deal would solve the intractable Northern Ireland border problem and its proponents say the EU would no longer have jurisdiction over agricultural policy, fisheries and justice. Britain would be able to resist closer political integration. True, freedom of movement would not end – from my own perspective, a good thing – but technically controls can be implemented if the government is able to prove “serious economic, societal or environmental difficulties”. Britain would also be able to shape its own rules on the financial sector. Norway plus advocates also claim it would mean significantly lower financial contributions, though this needs to be proven.

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There is one key issue of contention: state aid and policies of public ownership and economic interventionism, which Labour fears will undermine its ability to implement a transformative agenda. Common market 2.0 proponents point out that Norway has among the highest levels of state aid in Europe. On this, I defer to the economist Laurie Macfarlane. He suggests current rules do not preclude social democracy within certain limits but could represent a block on going further. Labour would have to test this argument in office: any bid to stop an elected government enacting its agenda would trigger a confrontation that, for the sake of democracy, Labour would have to win, appealing for international solidarity in the process. The arrangement might prove a stopgap. If it failed – for instance, if Labour’s proposals were blocked – it would have to end.

Is this kicking the Brexit can down the road? Yes. Is it desperate? Of course it is. But look, the social fabric of Britain is disintegrating. There is a housing crisis, child poverty is soaring, wages are stagnant, and our public services and infrastructure are falling apart. The more our relationship with a trading bloc becomes the central axis of political discourse, the less attention Britain’s social crisis receives, and the worse it becomes.

When May’s deal is voted down, Labour must push for a general election. But Norway plus may end up the only proposal that commands a majority in parliament. Labour supporters would be able to recall that what unites them is much greater than simply Brexit. Could it definitely be negotiated even if MPs vote for it? That’s not certain. But given the other unappetising choices on the plate, perhaps it is the only one Labour will be able to swallow.

• Owen Jones is a Guardian columnist