In Scotland, birthplace of Labour’s founder, Keir Hardie, the party was all but wiped out. The SNP’s anti-austerity, anti-establishment rhetoric won over voters who had always looked to Labour to defend their public services, but now saw the party supporting much of the Conservatives’ cuts agenda. In the preceding years they had seen Labour’s front bench advocating for tuition fees, PFI and war in Iraq. ‘It is the Labour party that left me, not the other way round’, said Mhairi Black in her maiden speech to the House of Commons as an SNP MP. Doubtless many of the 51% who voted for her in Paisley and Renfrewshire South feel similarly. For the last 70 years they have returned a Labour MP to Westminster; it will be a significant challenge to make Labour appeal to them again.

Jeremy Corbyn is, by some distance, the candidate best placed to try. His campaign has injected new life into Labour across the country: quite literally, given the tens of thousands who have signed up to support him, many of them young people. Labour membership is soaring at its fastest rate for 64 years, and it is Corbyn - with his town hall meetings overflowing even in SNP Scotland - who is providing the stimulus.

Polls suggest he is the most likely candidate to win back support not only from the SNP, but from UKIP and the Green party too. In target seats like Warwickshire North and Nuneaton, where UKIP support increased by 14%, Nigel Farage’s party almost certainly stifled Labour’s chances of gains from the Conservatives. Corbyn’s message - of investment in social housing, in local services, in people - is already providing a counter to UKIP’s anti-immigration narrative.

It is a narrative propped up on scarcity of resources, fuelled by the impact of the Conservatives’ austerity measures. These are policies that have saddled more pressure on local services and more debt on the poor and the young. Cuts to welfare, tax credits and public services, justified by the need to reduce the deficit, have been compounded by stagnating wages, less secure employment, increases in the cost of living and widening inequality. Only Jeremy Corbyn is calling out austerity for what it is: a lacklustre economic strategy that is enriching the richest while the poorest foot the bill.

Under Ed Miliband, Labour found itself ensnared by the government’s fetishisation of deficit reduction and stigmatisation of spending. Though the party was rightly critical of the pace and extent of the coalition’s cuts, it failed to challenge the underlying view that austerity was a fiscal necessity. Faced with the ballot box on May 7, it was perfectly possible for voters to believe Ed Miliband’s core message - that our society is too unequal and the Tories won’t make it better - and still vote for David Cameron’s core message: that there is a need to ‘make tough choices’ and continue to cut public spending.

Jeremy Corbyn offers a fundamentally different economic analysis. He argues that an end to austerity is essential, that the Conservatives have, quite simply, got it wrong. That matters partly because of Labour’s responsibility to stand up for those hardest-hit by the the current agenda. It matters partly because the party needs urgently to regain and consolidate support from those who have found it wanting on the left. But it also matters because a reasoned and credible counter-argument to the Conservatives’ economic strategy is our best hope of winning back floating voters.

Some have baulked at the idea that such centre-ground voters could ever be won from the left. But ‘the centre ground’ isn’t fixed. On the contrary, it is highly prone to change. For too long, Labour has opted to concede ground to the Conservatives rather than offer an alternative approach more conducive to the party’s aims. The result has been worsening confusion over those aims, alienating opportunism and a shifting of the centre-ground rightwards. Prior to Corbyn’s candidacy, the Labour mainstream saw most forms of public ownership or increased public spending as extreme, non-starter solutions. As the Welfare Bill made clear, these ties on social democracy are becoming untenable for Labour. If it continues to dance to the Conservatives’ tune, nobody will give Labour a look-in. If it stakes out new territory and leads people there from opposition, Labour could find influence long before 2020.

Far from leading a ‘hard left’ insurgency, Corbyn has won the most support from CLPs (including many that backed David Miliband in 2010), and has been polling best among every part of the Labour electorate: members, union affiliates and registered supporters. His ‘straight talking, honest politics’ have proven highly effective at communicating and energising people, even non-voters. It will be harder to persuade the rest of the country, but his burgeoning support base will be a vital asset.

Almost as strongly as on his anti-austerity platform, Corbyn has stood on redefining party membership away from a model resembling a magazine subscription and towards greater involvement in policy-making. A larger and more engaged membership would boost Labour’s ability to identify issues on the ground, to develop robust and representative solutions, and to advocate the party’s plans for government. As Corbyn’s ‘consultation documents’ have shown over the course of this campaign, policy infused with people enthuses people.

We do not know what will happen to the Conservatives over the next five years, and how ably they will sustain their fragile majority. We do know that Jeremy Corbyn has already enlivened and re-energised a Labour party that, until recently, was struggling on through perpetual decline. He is, perhaps, an unlikely figure to have done so. But he is now the only figure who can reconnect Labour to itself, and to the country.

His election would mark a hopeful, and vital, new era.

Jack Gamble is a Young Fabians member