Whatever happens next Thursday, an act of reconciliation will be necessary. Not between the winning and losing parties, but within one of them – bridging a divide that separates their supporters, both former and current, from each other. This gulf is not so much ideological as it is cultural or even tribal. The divide I have in mind is among the millions of people who either used to, or still do, identify themselves with Labour.

It’s been discussed often, but it’s rare to see it in a single room. That’s what I witnessed this week in the marginal seat of Dagenham and Rainham, where east London blurs into Essex. For the second time in a matter of days, I was eavesdropping on a focus group of voters, this time brought together especially for the Guardian by Ipsos Mori. In fact it was two groups, the first made up of leavers, the next remainers, sitting around talking politics with a facilitator in sessions of 90 minutes each.

There’s the Labour of the big cities, and there’s the Labour of the smaller towns, where change is seen as a threat

That split reflected something important about the constituency, which straddles both Brexitland and Remainia. It was here that the British National party used to pick up serious numbers of votes, where Ukip polled 30% in 2015, where working-class Toryism has roots that long predate the Thatcher era’s Essex Man. But it’s also here that many black and Asian families, graduates and the young have made their homes, often priced out of east London. The result is that you could guess before anyone opened their mouth which group was which: all but one of the leavers were white, all but one of the remainers were young.

That picture doesn’t just reflect the mixed and changing face of this one constituency, held in the last parliament by Labour’s Jon Cruddas. It reflects what used to be Labour’s wider electoral coalition, a mix rendered unstable by Brexit.

As it happens, there was not that much talk of Brexit itself: when leavers or remainers are only with each other, few feel the need to relitigate the familiar arguments. Instead, they talked about what ailed their area, what they wanted to see changed, how they saw the political parties and their promises. And on this, they were poles apart.

The first group – older, whiter, more working-class – liked Boris Johnson, or were at least ready to indulge him. They couldn’t stand Jeremy Corbyn, finding him weak, indecisive and old-fashioned. (If he was a TV programme, “he’d be Dad’s Army”. Where would he go on holiday? “Bournemouth, by coach.”) By contrast, the second group – younger, more diverse, often with a degree – were full of praise for the Labour leader, seeing him as “a man of principle”, while Johnson was “a racist”. The former were sceptical of Labour’s manifesto promises, worried there was no “magic money tree” and they were going to end up footing the bill via their taxes. The latter liked the free broadband and free tuition fees.

Most revealing was the difference in attitude to two new railway stations serving the area. Dave, a former trade unionist with memories of the old Ford plant in Dagenham, had joked that the area’s biggest problem was an “influx of Europeans”. He worried that the area was becoming too crowded, and new stations would only make it busier still. Meanwhile, David, a team leader in a communications company, was glad they were coming: they’d bring money and jobs into the area by making London closer.

In the same constituency, in the same room, you could glimpse the faultline that divides what some still like to call the Labour family. It’s the same gap that separates Grimsby or Oldham Labour from London or Manchester Labour. Crudely put, there’s the Labour of the big cities, graduates who see mobility, diversity and change as an opportunity, and there’s the Labour of the smaller towns, where those same shifts can look like a threat.

Play Video 0:46 Corbyn compares himself to Marmite: 'Some people like it, some people don't' – video

Of course, that divide not did appear for the first time on 23 June 2016: the writer David Marquand was worrying about “the progressive dilemma” three decades ago. But Brexit has widened it and dramatised it, not least because it’s pushed people to break a habit that had been passed down the generations – and change their vote. That leaves a question, what Cruddas calls “the outstanding question of reconciliation”, one facing social democratic parties across the world. How can Labour bring together two tribes that now seem to inhabit different worlds?

Some have argued that, despite its name, Labour should all but write off its old, white working-class base in the once industrial towns and organise itself instead around younger, socially liberal graduates in the major cities. Leave the left-behind leavers behind, and unabashedly become the party of climate-conscious, urban remainers: after all, the first lot are dying off, the second are the future.

That’s a crude summary, I know, but you get the gist. Yet that approach grates on every progressive instinct, that a party of the left should be the party of working people, not just modernity’s “winners”. It fails a more basic test too: social democrats can’t win power without working people’s votes.

But if the task of binding those two groups into a single party has always been a challenge, what Cruddas calls “the Brexit trauma” has made it infinitely worse. Was there anything Labour could have done to keep both leavers and remainers on board after the referendum? I’ve spoken to MPs in leave seats who believe there was. It would have meant Labour crafting a compromise position – in effect, a soft Brexit – and advocating it consistently and clearly. Both leavers and remainers would have had to give up something, but with persuasion maybe both could have been won round. The current stance, of neutrality in a second referendum, does not quite cut it, says one MP, because the outcome will see one camp winning and the other losing, rather than both sides meeting halfway.

For myself, I cling to the view that Labour could have stuck to a remain stance and still retained the support of leavers. But it would have required something like a rerun of Tony Blair’s 2005 “masochism strategy”, when he put himself in front of hostile audiences who lacerated him for the Iraq war, absorbing all their invective, gaining grudging credit for facing his critics and sticking to his convictions. If Corbyn had done that in leave-voting seats, straight after the referendum, maybe some of those Labour leavers would not be preparing to abandon the party now.

Labour has a strong economic plan. But it still has to shift voters’ faith in austerity | Larry Elliott Read more

What both approaches would have required is strong leadership and a compelling plan to rejuvenate the towns, a sign that Labour had deeply understood the anxieties that fuelled that 2016 vote. Free tuition fees and discounted rail fares do not quite send that message, no matter how appealing they might be to young or metropolitan voters.

And yet, those MPs who, in their own seats, have to walk this high wire, winning over the two camps, are not wholly despondent. Across both Dagenham groups there was agreement on the NHS and on the need for investment in public services and the economy. Surprisingly, perhaps, there was some convergence on crime too. It was not the leavers who demanded that those guilty of knife crime serve full, harsh sentences, but two young black men in the remain group. That points to a possible bridge that might join Labour’s two tribes.

Talk to Lisa Nandy, seeking re-election in Wigan, and she recalls the slogan which, more than any other, once brought Labour’s two wings together: “Tough on crime, tough on the causes of crime.” That, says Nandy, “spoke to both the middle class and those who were working class to the core. It reassured both of them.”

The bitter end of the New Labour project has obscured how it began and what made it successful enough to win three big majorities in a row. But its earliest lessons may need to be learned all over again.

• Jonathan Freedland is a Guardian columnist