Meet Clive. He is retired, a devoted monarchist – he has a mug commemorating the birth of Prince George – is worried about immigration, has always voted Labour, but is worried about Jeremy Corbyn. As a result, he voted for Ukip in the Oldham by-election. His postal vote arrived the day the Labour leader announced he was “not happy” with “shoot to kill”.

Meet James. He voted Green at the last election. The only immigrant family he dislikes is the Windsors. If he could vote in Oldham, he would vote enthusiastically for Labour.

This, rather than shadow cabinet rows or unease in the parliamentary party, is the divide that is hurting Labour. Like most European social-democratic groupings, Labour is an uneasy coalition between its industrial or ex-industrial core and what Michael Frayn called “the Herbivores”: “do-gooders . . . readers of the News Chronicle, the Guardian and the Observer . . . signers of petitions, the backbone of the BBC”.

Taken together, that electoral coalition was, for Labour, enough to secure at least second place throughout most of the latter half of the 20th century. When the party has been able to add votes from the so-called aspirational classes – those who were excited by hire purchase and ITV in the 1950s, Right to Buy in the 1980s and now Help to Buy under the Conservative-led governments since 2010 – it has been able to disrupt Britain’s Conservative hegemony, albeit for relatively brief periods (excluding 1997 to 2010).

Since the financial crisis, that division has broken down. Under Ed Miliband, as the academic Tim Bale put it, Labour was divided between “people who drink wine, and people who drink lager”. Wine drinkers drifted away to the Green Party. Lager drinkers trickled away to Ukip. The result: thumping defeats across England and Wales.

Under Corbyn, that Greenward drift has gone into reverse. Labour’s new leader is catnip to the Herbivores. The Ukip trickle, however, is turning into a flood in some places. In Oldham West and Royton, Labour sought salvation in the seat’s Asian vote – but white working-class constituents defected in large numbers, to Nigel Farage’s party, or simply by staying at home. It is a journey that Labour MPs have seen voters make before. “In 2005 it was: ‘I’ll vote Labour one more time,’” recalls one grandee. “In 2010 it was: ‘I’ll stay home.’ In 2015 it was: ‘I think I’m voting Ukip.’”

Jeremy Corbyn’s challenge is to find a way to bring together his sympathetic Herbivores and Labour voters, in towns such as Oldham, who are tempted by Ukip, and – if that wasn’t hard enough – win some Tory voters in the process.

Fifty-six years ago, after a third successive election defeat, Denis Healey told the party conference that Labour would “never get power unless we close the gap between our active workers and the average voter in the country”. That gap is now wider than it has been in many years. Polling commissioned by the freelance data guru Ian Warren, who worked for Labour in the 2015 election, shows that Corbyn’s Labour Party is at variance with every demographic in every region across the country on every major issue, from immigration to social security.

The media frenzy over party divisions and Corbyn’s particular vulnerability to Ukip obscures a wider problem for the British left: whether any politician can hew together the three groups necessary for a left-wing majority in the Commons. It may be that, whether the choice is losing votes to Ukip and the Tories, or to the SNP and groups to Labour’s left, the party must simply decide which direction it wants to turn to face the sunset.