Two parties, a chasm of differences separating them, but fused together whether they like it or not. Here is a description that could surely apply to either the Conservatives or Labour. Intra-Tory hatreds nurtured since the toppling of Margaret Thatcher are surfacing with explosive effect thanks to the EU referendum.

Tory MPs conspire to undermine their leadership, and plot with little subtlety for the downfall of David Cameron if Britain opts for Brexit or a narrow Remain. Tory Brexiteers look to Scotland for inspiration: where a referendum fails to settle a constitutional issue, and politically galvanises the proponents of the exit option in a “neverendum”. “I don’t want to stab the prime minister in the back – I want to stab him in the front so I can see the expression on his face,” were the reported comments of one Tory MP, who expressed his hope that Cameron would be caught “with a live boy or a dead girl”. Tim Montgomerie – Iain Duncan Smith’s former chief of staff, who quit the Tories this year – imagines a realignment of British politics, with the Conservatives dividing three ways: a “patriotic right” party, a “socially just, economically conservative” party, and a party of “social and economic liberals”.

Labour’s internal strife, meanwhile, has been temporarily calmed by two factors: a referendum that has concentrated minds, and local election results – peppered with successes – that were nowhere near as bad as predicted (if not, as Jeremy Corbyn himself noted, good enough for a party aspiring to win in 2020). There was a parliamentary plot to force a leadership contest after the referendum, rally around a “soft left” contender as a stopgap, and – by dubious means – keep Corbyn off the ballot paper. But this plan is dead.

That does not mean divisions have disappeared. One senior MP – on the right, but constructive – identifies two groupings of parliamentary opponent. One faction believes that Labour is probably unelectable under the current leadership; the other concurs, but would be vehemently opposed to a Corbyn premiership assuming power in any case. If Labour looked likely to come to power with its current political direction, in other words, they would sabotage its prospects. And this is why the MP believes a formal split, at some point, remains a distinct possibility. The other mooted option is an increasingly likely early election, called when Labour remains unprepared for office, leading to a haemorrhaging of seats from an already low base, forcing Corbyn out and routing the left.

Some on the party’s right – not least its “old Labour right” – harbour ambitions to reconquer the party and crush the left. The reckoning would be “brutal”, one of their number promised when Corbyn was elected, “putting the left in a box for 30 years or out of the party.” But the right have offered no convincing route to electoral victory on their terms. They sometimes behave as though Corbynism is collective madness, rather than part of a trend sweeping the western world. In countries like Britain and the United States (where Bernie Sanders has become the most successful socialist in US history in his battle against Hillary Clinton), the split happens within an established party. In, say, Spain, the split happens outside: with the social democratic PSOE challenged by a more radical coalition led by Podemos. And the more perceptive elements of Labour’s right accept that it was their ideological vacuum which allowed Corbyn to triumph against all the odds.

Across the country, the Labour coalition has fragmented. In the aftermath of last year’s election defeat, those Labour supporters who expressed a view were almost evenly divided about whether the party should move left or right. Corbyn is often portrayed as the figurehead of an unrepresentative Labour membership, but in the final stages of the contest, polling suggested he had a decisive lead among Labour voters, not just members.

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In the last general election, younger voters plumped decisively for leftwing options (quite unlike the early 1980s, when Thatcher won over the under-25s), while older voters increasingly veered towards the Conservatives. Take specific issues. Younger voters in major towns and cities are more sympathetic to diversity and immigration; older working-class voters, particularly in towns battered by deindustrialisation, are often hostile. Labour embracing either an anti or a pro-immigration stance has the potential to alienate either group. Already, Labour’s traditional base has fragmented in multiple directions: to the SNP, Ukip and the Greens. Straddling these multiple divisions is a formidable challenge for any Labour leadership, whether it leans left or right.

That’s why Labour figures on both right and left – from Chuka Umunna and Jonny Reynolds to John McDonnell – are increasingly embracing the cause of proportional representation. They are uniting in order to divorce. One prominent figure on the party’s right alluded to the “Spanish solution”. PSOE and Podemos are standing against each other in the upcoming Spanish general election, the latter with a slight lead over the former. If left-of-centre parties win a majority in the Spanish parliament, they will form a coalition.

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Under proportional representation Labour would split into a centre-left and a left party. “Both would stand against each other and compete, but then end up in government with each other,” the senior figure suggests. Rather than an acrimonious battle for the leadership of one party, both would be free to stand independently. A friend of the late Robin Cook tells me this was the former Labour foreign secretary’s own view: PR leading to divorce, with a wrestle over who keeps the “Labour” name and tradition.

The road to proportional representation is fraught, of course. A minority Labour government at the very least would need to be formed. Getting there could involve making difficult deals with other parties. A new approach would be needed to win over those (including myself) who voted against the Alternative Vote in 2011. Progressive voters would be subjected to a fear campaign portraying a vote for PR as a vote for 60 Ukip MPs.But it is worth asking the question. If Labour did not exist, would Corbyn and Peter Mandelson join forces to found it? If the Conservatives were founded tomorrow, would it really be an alliance of Cameron and John Redwood? Britain has fragmented, and so has politics – but the electoral system makes us pretend otherwise. For both Labour and Tory warring sides, proportional representation would set them free.