Jarvis Cocker doesn't just like tights. It's bigger than that. This is a man who really knows his hosiery. An authority, as well as an aficionado. A white woolly pair loom large in his latest project: a feature-length patchwork of archive footage of Sheffield's steel works with a live soundtrack. A hand slides its way up the gusset. We're close in on a hillside fumble in the 60s, with spectacular backdrop of factories below, chimneys erect and steaming.

"That bit was mine," confirms Cocker, sitting beside his collaborator, film-maker Martin Wallace. Wallace, as smooth and compact as Cocker is stretched and furry, nods. Cocker continues. "I just really liked that shot of the grass stain on her knees. And that they were those kind of meshed ... what do you call them?"

Like fishnets, but thicker? Cocker's glasses glint. "They weren't fishnets. They were knitted tights, really, with a very pronounced rib weave. And I thought: 'Oh, that lattice-work looks like a gantry, like you'd see on a scaffolding or something.' So I got very excited by the tights, and the link with the steel girders."

The sensuality of heavy industry is a leitmotif in The Big Melt, which opened the 20th annual Sheffield documentary festival last week. Cocker, still a dapper giraffe at 49, stood centre stage, flanked by members of Pulp and the Verve, as well as a harp, flutes, a man playing a saw, and, for spells, a youth choir and a brass band. Behind them on the screen: clanking pistons and oceans of ore; sweat-soaked stubble and endless rivets. The score was big on reverb, more rave than concert, with the odd bit of Stars on Sunday, This is Hardcore, Sheffield: Sex City and the soundtrack from Kes. As the conductor, Cocker crawled and thrusted and squatted and wiggled (I bet Simon Rattle never star-jumped to start up the strings). At the end he explained to the crowd at the Crucible that he had hoped to simulate the steel-making process: to heat us up, to melt together, to become one. To make us – a classic Cocker pause here – hard.

Jarvis Cocker's The Big Melt at Sheffield Doc/Fest. Photograph: David Chang

He looks slightly fragile the next morning, en route back to London. He's about to jump on the train and is lugging a holdall, a Daunt Books tote, a guitar case patched up with duct tape, so we get straight to it. Are the people of Sheffield more plugged in to their essential elements, on account of this relationship with steel? "Yeah. It's a primal thing. That's why we ended up with this molten footage at the end. That's still happening in the centre of the Earth. At one point the Earth was just a ball of molten stuff. So that thing of melting it down and taking it back to that: it is the primal state, innit."

He sucks on a cup of tea, and Wallace chips in. "It's also kind of magical. Once they'd nailed how to make it, it was like: 'Oh, let's have a steel cup, some steel glasses.' It really opened the door to change the world, albeit to try and batter other people."

The film (imagine a really trippy educational video) includes a tour of a munitions factory during the war, and a propagandist cartoon imagining the horror of a world without steel: no car for Dad to drive in, no nails for baby's cot, and, most awful, no pins to keep Mum's hair in check. It has an orgiastic graphic of exports, great arrows seeding Sheffield's best around the globe.

"There was a soundbite we didn't use," says Cocker. "'Every time you sit down to a square meal, you're eating steel.' Which sounds like you'd break your teeth but it would always bring a tear to my eye. The model has changed from when I was at school. We're not living in that any more, where real things are exchanged for real things. We've entered the abstract capitalism era where we don't know where money is coming from or what it does."

This nostalgic currency, the temptation of cliche, is what made Cocker initially drag his feet. "Growing up in Sheffield you get things about steel rammed down your throat the whole time. What's the equivalent in Liverpool?" He turns to Wallace. "The Beatles." Cocker smiles. "Maybe it's similar because the Beatles are really good but you don't wanna talk about the them the whole time. You're like: 'Oh I'm not like that. I'm not a steel person.' So I just thought, whatevs. Not whatevs, but I didn't know if I could do anything interesting with it."

The night before, Cocker said he was now reconciled to the fact steel had helped make him what he was. Yet it seems strange someone so intimately associated with their hometown would shy from identifying themselves as a product of their environment.

He musses his hair thoughtfully, fingers lingering on the fringe. That wasn't quite it, he thinks. "You're aware you're dealing with something that is very important. You don't want to fuck it up because that would just be very sad. It's not something be entered into lightly. You can get weighed down by it, the history can be oppressive. And that's why we were kind of wary about getting into the politics."

It's true; though Cocker speaks about the spookiness of being raised in a place that increasingly felt like an abandoned film set, The Big Melt shies from sadness, instead going full throttle to praise steel and its peripherals. "By involving the other musicians from Sheffield, it was like we were taking that base from the material and messing around with, making it into something new. An entertainment alloy." He grins at the coinage.

What finally clinched it for him was seeing a bit of footage – which ended up being played, like the tights, on a loop – in which a young lad queuing for his shift flicks the V at the camera. "I rewound it, and it reminded me a bit of Kes, and then I thought that maybe it's not about steel, it's the attitude it made of people, the spirit."

So what's the actual alchemy? What happens when steel meets soul? "Well, it was just super-intense extreme conditions. The idea of even being in a place with a massive ball of flame coming at you most of the day, with an ear-piercing noise. That was your working environment! That's just crazy."

That's also not so very different from the working environment of the pop star. There's the steam and the heat, the twiddling of knobs and levers, the fetishisation of kit, the strobing lights, the primacy of body language above the roar. And, after, the pubs and the bunk-ups.

"I think I understood from working on the film why people drink so much more than they do in the south," says Cocker. "Partly it was a particular thing of losing a lot of moisture, but also after doing that all day you've got to kind of wind down. And maybe also this thing of loud noise. First of all, everybody was deaf, and then also they were exposed to extreme sounds. Sheffield's always been a town of extreme bass. It must have got summat to do with it. That kind of forms what you're like. You might not appreciate some bass if you've not heard it. But if you've heard it echoing through the city at night you'd think: 'Oh, that's interesting, let's do something with that.'"

Cocker grins and Wallace nods again. They're a groggy Holmes and Watson, solving the mystery of why Sheffield rocks. The answer was there all along. It rocks because of the rock.