How does class politics survive a full-blown culture war? This is the crux of Labour’s current dilemma. The basis of its political vision is that the economic interests of the majority are not only different from those of the elite, but on a collision course with it. This is pithily summed up by the party’s slogan: “For the many, not the few.” Yet the Brexit culture clash smothers any discussion of the real divide in British society, let alone how to overcome it.

After the referendum, Labour had a strategy to deal with this. It accepted that while remain lost, the leave triumph was narrow, and therefore there should be a close relationship with the EU. This positioning granted the party permission to pivot back to talking about domestic issues. It prevented Theresa May turning the 2017 contest into the Brexit election she sought; the party instead could fight on issues – like taxing the rich and big business to invest in the economy, tackling student debt, and public ownership – for which there was majority support. Had she succeeded, the Tories would not have been deprived of their majority, and Britain would already have left the EU on the terms May desired.

Since the election, the middle ground on Brexit has been obliterated. According to the latest polling by Opinium, the percentage of those “supportive of a Brexit where the UK is closely aligned with the EU” is a derisory 13%. An equal share – 39% – backed either remaining in the EU on the one hand, or a so-called clean break on the other. For those remainers who sought to make the result work, three disastrous years have stripped them of patience; for leavers who were promised that no deal was better than a bad deal, before being presented with a very bad deal indeed, only a complete rupture now amounts to genuine Brexit.

Which brings me to Labour’s current internal debate. The group now demanding that the party shift to a position of backing a referendum with remain on the ballot paper, no ifs, no buts, is far from restricted to Jeremy Corbyn’s internal rightwing opponents. It includes, in the shadow cabinet, longtime allies and leftist stalwarts John McDonnell and Diane Abbott as well as “soft left” members such as Keir Starmer and Emily Thornberry. It takes in the pro-Corbyn Scottish and Welsh Labour leaderships, and the London mayoralty; key unions, such as Unison and the GMB; and Labour members, over half of whom didn’t vote for their own party in the European elections according to YouGov – which accurately predicted the results of the first and second leadership elections. It is Labour’s de facto position to accept a referendum in all circumstances; it’s just not being spelled out clearly or coherently enough, and consequently isn’t cutting through to ever angrier remain supporters. That doesn’t mean adopting Tom Watson’s position of supporting the EU as a socialist project – self-evidently it isn’t – but rather fighting for remain and reform.

At Labour’s September conference – or in a snap election, in which the party manifesto is decided through the “Clause V” process – it is inevitable that a clear position of backing a referendum with remain on the ballot will be adopted, likely with a commitment to campaigning for such an outcome. The danger is, if the leadership waits that long and has this new position imposed upon it, remain-leaning voters will say, “Well, you don’t really mean it, I’m not coming back.” Supporters of the existing position reassure themselves that many voters, faced with the prospect of Boris Johnson and no deal, will return to the fold in any case. But that level of triangulation is a big risk. The day after Labour’s battering in the European elections, a letter from the leadership to the parliamentary Labour party declared, “We are ready to support a public vote on any deal”; by the end of the week, it had rowed back to a more ambiguous position. The party is in danger of zig-zagging incoherently to what is an inevitable endpoint, amassing further contempt from both sides of the referendum divide as it does so, and suffering only the downsides of a new policy without reaping the benefits. There are those of us who defended a compromise Brexit position out of conviction, rather than partisan loyalty. We have lost the argument: that is to be both mourned but also accepted.

The discomfort of Labour MPs representing leave seats is understandable. For too many others, a false dichotomy that pits “working-class leaver” against “middle-class remainer” distorts their analysis. They look at centrist, London-based remain leaders – some of whom have cynically used Brexit to undermine the Labour leadership (disillusioned members of the People’s Vote campaign openly tell me that Blairites have used the issue to regain political relevance) – and extrapolate. But what of the majority of working-class people – even using the flawed definition of “working class” used by pollsters which is skewed in favour of pensioners and which excludes jobs such as nurse and train driver – under 35; or most black and minority ethnic working-class people; or indeed so many Scottish working-class people who voted to remain? What of the fact that most of Labour’s voters in its leave seats voted for remain: how does it win those constituencies without them? Labour rightly boasts of one of the biggest mass memberships in western Europe: what use is that if they are so demoralised they are not only reluctant to campaign for their own party, but also prepared to vote for others? The evidence shows Labour-inclined leave voters give Brexit far less priority than other pro-Brexit supporters: could not a transformative economic agenda prove more alluring to these voters than a changed relationship with the EU?

Unite, the nation’s biggest union, is frequently demonised: from the perspective of Britain’s elite, this is entirely rational – without its leadership, Labour’s political shift would never have happened. It exists to represent its members, and it hears that its shop stewards, not least in regions such as the East Midlands, oppose a new referendum. Its leaders fear, justifiably, the intensification of a culture war that both pushes out class politics, and has every likelihood of being won by the right anyway. Yet it is impossible to ignore the fact that not only are many working-class and middle-class Labour supporters alike now antagonised by the party’s failed Brexit compromise; but that Labour cannot win permission to talk about its radical domestic policies unless it abandons its fudge.

It will clearly be forced to do so anyway, so why not suck it up now and make the best of it?

For those of us who believed in a Brexit compromise, the culture war has been both alarming and disheartening: the fears that a second referendum – for which there is no current majority in parliament in any case – would pour petrol on to raging political fires are justified, never mind the high risk of leave winning all over again. But a clear position will provide space to refocus on now marginalised economic issues. Corbyn himself recognises a change is necessary; but a decisive public shift hasn’t yet been made.

He told this week’s shadow cabinet that consultation with unions and the party’s National Executive Committee must take place to build a consensus position. Just consider this, though: the Tories openly panic about “Corbyn by Christmas”. Their nightmare – a transformative government that terminates the failed economic experiment initiated by Margaret Thatcher – is entirely plausible. Yet many allies of Corbyn now privately fear the entire project is in real danger. It may well be that another election will galvanise Labour’s support, as the last one did, regardless – aided by the menace of Boris Johnson. But unless Labour states clearly, boldly and unapologetically that its attempt to bring the country together with a unifying Brexit compromise has been destroyed by a shambolic Tory government; unless it states that since “no deal” beckons, giving the public a final say with remain on the ballot paper is unavoidable; unless it does all that, then the best opportunity in the western world to decisively break with market fundamentalism is inarguably threatened.

• Owen Jones is a Guardian columnist