Lecturing on the supreme importance of electability the other day, Gordon Brown forgot a historical detail. Pacing the stage like a man stuck on a malfunctioning treadmill, the former prime minister neglected to explain what really happened in 2010.

Not his defeat. That bit of reality will not be defied. New Labour's last, dismal paragraph was definitive. Nevertheless, amid his talk of duty, high ideals, and doing “what is necessary to get back to power”, Mr Brown ignored a pertinent fact about his loss: in the contest for worst-ever Labour performance, he was a bigger disaster than even the scorned Ed Miliband.

Not by much, to be sure. Mr Brown achieved 29 per cent of the vote while his former protege got just 30.4 per cent. The fact remains that Mr Miliband secured his crumb of comfort while committing the cardinal error – according to hordes of his former allies – of taking his party “too far” to the left.

As revisionism goes, it's fairly typical. For most of his time as leader Mr Miliband was not expected to win an election at the first attempt, such was the scale of the Brown catastrophe. Even when caught up (like the rest of us) in the illusion of a tight race, Labour's 2015 hopes rested on scraping together a government from a hung parliament. Still Mr Miliband did better than Mr Brown.

He did better, indeed, despite certain events in Scotland and the loss here of 40 Labour seats that had bolstered the tally for his old boss. He did better than his predecessor, in terms of share of the vote, despite Ukip's depredations. So who is Mr Brown, exactly, to be “intervening” to hinder Jeremy Corbyn, or assure us, in the usual code, that a left-wing leader can never be “credible”? That lordly sagacity did Labour a fat lot of good in 2010.

It goes without saying that, listing to the left to varying degrees aside, Mr Miliband and Mr Corbyn have precious little in common. The usual checklist of affronts to right-wing propriety – Trident, borrowing, taxes – would in other circumstances have seen them in different parties. What remains the case, amid the thud and blunder of the leadership contest, is that they have a mutual interest in Labour's future; Mr Miliband for what might have been, Mr Corbyn for might what be. Issues of left and right, in that context, are diversions.

The question has already become a cliché: what is Labour for? In fact, it's the wrong question. Given what became of Mr Brown's leadership, given what became of Mr Miliband, given the ascendancy of the SNP, the destruction of the Liberal Democrats, and the Ukip phenomenon, a better inquiry would be this: where is the space in politics now for Labour, this “left-of-centre” (according to taste) pan-British party?

The fragmentation of politics will not be halted because Mr Corbyn's objections to austerity strike a chord. The question of Scotland will not disappear because the favourite for the Labour leadership is, he tells us, “a socialist not a Unionist”. The appeal of Ukip will not be blunted should Labour attempt a little more appeasement. Even the revered centre ground is no longer a refuge. Those in his party who detest Mr Corbyn have failed to notice what has become of that construct.

The old Westminster duopoly is reaching its end. Mr Miliband's inept handling in the spring of questions arising from the possibility of a hung parliament was inadvertent proof. All agreed (not knowing the half of it) that Labour could not win alone. So how did Mr Miliband mean to form a government? The question he would not or could not answer – nor could David Cameron, back then – was fundamental: how would he come to terms with a new reality?

But, you might say, the Tories got their majority. They govern unaided. The old system still works. It works in the same way a mirage is effective. The duopoly's joint share of the Westminster vote has been ebbing away for a generation and there is no sign of the process being reversed.

In 1992, the Conservatives and Labour divvied up 76.3 per cent of votes cast. Historically, that was nothing: Margaret Thatcher and Jim Callaghan achieved 80.8 per cent between them in 1979. Yet when Mr Brown was crushed, the joint party share was 65.1 per cent; this year (credit to Mr Miliband) it was a mere 67.3 per cent. The centre ground, if such is your definition, is eroding.

The problem is intensely practical for anyone who seeks to lead the Labour Party. The assumption is, inevitably, that lost voters can somehow be returned to the fold. Take the obvious question, one we have heard asked for weeks. “Can Corbyn/Burnham/Cooper/Kendall win back Scotland?” It is fair to say that in their flying visits, acclaimed or derided, not one of the four has offered a coherent answer. Nothing has changed since May: left or right, they have no idea what became of the party's Scottish vote.

If and when he wins the leadership contest, Mr Corbyn will have to deal better with the issue than he has managed hitherto. No doubt he will make a dent in SNP support, at least to begin with. No doubt his challenge to the prevailing economic idiocy will appeal to some of those who gave up on Labour. But if all he means to do is trump Nationalist rhetoric he will find he has arrived on the scene a little late. If his MPs meanwhile undermine his leadership, as appears to be the lunatic plan, voters will surely sit tight. A brave lame duck is still a lame duck.

How much autonomy would Labour in Scotland be granted by any of the prospective leaders? How much autonomy does Kezia Dugdale, the latest Scottish leader, actually want? Would she support Mr Corbyn, rebel, or attempt to believe that Labour in Scotland could still be rebuilt amid the internecine mayhem promised by Westminster factionalists? The questions are rhetorical. No answers have been forthcoming.

Disunity is a symptom of Labour's problems, not its cause. Arguments over who most truly represents the party's “values” are irrelevant when the ground is disappearing beneath its feet. What remains of traditional Labour territory? Not much. What does the party offer, from right or left, to voters who have few traditional loyalties that those voters cannot find elsewhere? In reality, precious little beyond a belief in power and in “revival”. The binary logic of politics is failing.

For now, the SNP and Mr Corbyn are merely postponing their disagreements. It is a matter of tactics and principle on either side while the arguments against austerity prevail. That won't last. Mr Corbyn believes that his “radical alternative” will prove “attractive to working class Scots to stay within the UK”. Obviously enough, the SNP think otherwise. As they will always maintain, a lopsided Union guarantees Tories.

Mr Corbyn's party is stuffed, in any case, with people who despise him and his alternative. Those veterans of electoral failure are not going away. When the time comes for Scots to choose, that fact will be abundantly clear.