Our politics are forged by a complex, often contradictory range of factors: the values of our parents, our experiences and ambitions, and our social circles, jobs and circumstances. Our communities too – and that certainly goes for my corner of Stockport, close enough to Edgeley Park to hear the roar of Stockport County on a Saturday afternoon.

Like so much of England, it may as well be a different country to London: friendlier, although more suspicious of difference. My ward was the second poorest in the borough (though before I’m accused of affecting a nonexistent working-class upbringing, my father was a white-collar local authority worker and my mother a university lecturer) – and here, in a community with few immigrants, Ukip – a party that blames low wages and the lack of secure jobs and affordable housing on immigration – came a triumphant second in May’s local election.

Here is a failure of the left. People want answers to their unaddressed everyday concerns, fears and insecurities: a vacuum has to be filled. Which brings me to Jeremy Corbyn’s campaign for the Labour leadership. This quietly spoken man has provoked two main responses. On the one hand, his increasingly energetic and enthusiastic grassroots campaign has now been endorsed by Unite, the country’s biggest trade union, which organises predominantly private-sector workers. His Labour opponents are genuinely rattled; this is not going according to the script.

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From the right, on the other hand, it is all belittlement and ridicule, portraying Corbyn as a guarantor of interminable Tory governments. It is worth responding to this. The right, in triumphalist mode, is bemused and irritated that the left should even still exist, and will spin anything to its advantage. If Corbyn does badly, it will be taken as evidence that the left is all but extinct; if he does well, it will be evidence that Labour is unelectable.

Politics should, of course, be about policy rather than personality – but that is not the world we live in. There is a long tradition of left figures who are charismatic and deliver rousing speeches but who – like George Galloway – are easily portrayed as demagogic. They can rouse the affections of the already convinced, but few others. When they are the object of personal attacks, they attract little sympathy, and tend to respond in kind.

Corbyn, on the other hand, has a good shot at the title of most self-effacing and humble politician in parliament, and certainly for being the lowest expenses claimer among his colleagues. That helps shield him from the personal attacks that are normally dished out to figureheads of the left. While other leadership candidates compare each other to the Taliban, Corbyn eschews the vitriol that is standard fare in modern politics.

But the test of the Corbyn campaign, for me, is the extent to which it can rebuild a left with popular appeal that offers a coherent, viable, attractive alternative to the status quo. That means winning over some of those who voted Ukip, even some who plumped for the Tories, and certainly those who did not vote or who opted for the Greens or the SNP. Indeed, if Labour is serious about winning in Scotland again, it would have been disastrous to exclude Corbyn. The SNP would relish nothing more than a Labour contest composed of three pro-austerity, pro-Trident candidates, enabling Nicola Sturgeon to convincingly tell ex-Labour voters that there is no place for them in their old party.

While other candidates compare each other to the Taliban, Corbyn eschews the vitriol that is standard in modern politic

It also means popularising marginalised policies and ideas. On issues from the living wage to public ownership, public opinion is on Corbyn’s side. The challenge is to overcome the sense that such policies can never be delivered.

The left will win by building an alliance of low-income and middle-income people: that is, the majority of society. A living wage is good not just for workers but for businesses, with better-off customers, and taxpayers, who will spend less subsidising poverty wages. A homebuilding programme not only reduces the social housing waiting list, it creates skilled jobs and means less public money wasted on private landlords. Policies could promote home ownership without flogging off desperately needed social housing.

Emulating the industrial strategy of Germany would not only create skilled jobs, but a thriving research and development sector for graduates. Public investment banks could support local businesses currently starved of loans. Concerns over immigration could be addressed through an “immigration dividend”: extra public money for services going to communities with higher levels of migrants. Middle-class commuters resent some of the highest rail fares in the western world, and their taxes are splashed out on far higher subsidies than in the days of British Rail. Public ownership – this time democratically involving passengers and workers –would benefit them.

The left is generally portrayed as archaic, infantile or both: a coalition of the naive (if young) or of dinosaurs (if old), with few inspiring ideas relevant to the complexities of life in 2015. The risk is always of playing to these stereotypes, resorting to slogans and defensive postures (“Stop the cuts! Stop privatisation!”), rather than going on the offensive with a compelling alternative.

But – without sounding all New Labour – there is now an opportunity for forward-looking policies that benefit and appeal to working-class and middle-class Britons alike. A rare platform is on offer to the left that confounds expectations by looking modern and dynamic, not trapped in a remote and unfamiliar past.

Corbyn faces incredible odds, and will continue to be belittled or demonised as the occasion suits. But I think back to those people I grew up with. They need hope and better answers than those peddled by a ragtag bunch of rightwing charlatans. Maybe – just maybe – if the left gets its act together, that hope might finally be on offer.