"This is the mother, the metal mother," says Jay Millar, examining a brilliant silver disc on the machine floor of United Record Pressing in downtown Nashville. "And the mother is where it all starts."

Fifty years ago United stamped out the Beatles' first US single and dozens of Motown hits followed by countless 45s and 33s through the 1970s and 1980s. Today more than two dozen vintage presses stamp out albums in a hissing, whirring display of a century-old technology that not only refuses to die, but is roaring to life. Nashville can lay claim to being the world capital of vinyl, and the city's music industry is struggling to keep up with the demand.

United Pressing is the largest vinyl pressing plant in the US, with a close relationship to Jack White's production emporium Third Man Records nearby, as well as Nashville's booming analogue music recording scene.

Next year the firm will add 16 presses that should boost daily output to 60,000 records. Millar, director of marketing, won't say where they found the presses – manufacturing of vinyl records ceased in the early 1980s and competition for presses comes from surprising quarters. The last few machines capable of cutting a metal mother – the stamp that imprints the plastic vinyl – were purchased at auction by the Church of Scientology, whose followers believed that the best way to preserve speeches of the master, L Ron Hubbard, for posterity was a 33⅓ album.

Scientologists are not the only ones returning to vinyl. After years of bruising format wars that have halved the size of the music industry, consumers appear to have made a decision. As CD sales and MP3 downloads decline, streaming services and vinyl sales are growing. "So now we've got digital, peak of the convenient, and vinyl, peak of the experience," says Millar. "We're running 24 hours a day, six days a week and still not meeting demand." As of mid-June, vinyl sales in the US were up 40% over the same period last year and look set to easily exceed 2013's 6 million total for the year. It's worth remembering that in 2007, vinyl sales struggled to reach 1 million.

It's understandable that Nashville analogue audiophiles such as Jack White or Black Keys would want their music pressed but now even mainstream pop artists such as Taylor Swift and Beyoncé want their music available in LP format. Demand is so great that production time has doubled to 12 weeks, and record companies now won't schedule a release date until they know they can get the vinyl.

If any album has come to symbolise the vinyl boom it's Jack White's recent Lazaretto, the top seller of the year. Packed with novelties, including one side that plays from the centre to the edge, it shifted 40,000 LP copies in the first week of release in June, more than any release since 1991, and is still selling 2,000 copies a week.

Third Man Records, first established to print the White Stripes catalogue, is emblematic of a musically resurgent Nashville, home to energetic rock'n'roll and psychedelic scenes. It's testament to White's obsession with sound.

Neil Young recorded his recent A Letter Home in a phone booth-like contraption near the entrance. There's a straight-to-acetate cutting machine from James Brown's King Records in Cincinnati; a glass cabinet in which toy monkeys dance to new releases. Red walls face one direction, yellow another. Slender women in yellow-and-black Third Man livery move between offices. There are several large stuffed animals, including one that looks like a yak.

"Actually it's a tahr," says Ben Swank. He and Ben Blackwell are White's consiglieres in Third Man operations. The trio are architects of Third Man's "Your Turntable's Not Dead" campaign and a direct subscription service that offers a monthly mailout of vinyl releases. Since moving from White's native Detroit to Nashville in 2007, Third Man has put out nearly 300 records, mostly singles.

"Jack does more of the Americana, Ben and I do more of the rock'n'roll and punk. We're still predominantly a 45 label. We try to be spontaneous. Got the master? Let's put it out!"

With studios here tied to Black Keys' Dan Auerbach and Brendan Benson, Swank says Nashville, with its long association with country music, is re-emerging as a centre for artisans. "There's a community here – a mom-and-pop thing," he says. "It's not that we shun anything current. It's just more romantic for us to use a ribbon mike or analogue tape. There's an aspect of working harder for something that gives it more value."

The success of Nashville may be to do with the city's innate conservatism. Country music, for instance, continued on eight-track long after other genres abandoned the format and, like survivors in a nuclear apocalypse movie, recording and mastering studios were never dismantled. "We're in a sweet spot," Swank adds. "People still want objects with personality."

But there's residual anxiety that the analogue revival is temporary. "Everything comes back once before it goes away for ever," says VH1's Bill Flanagan. "If it's just a nostalgic or hipster-elitest thing, where does that leave us in 10 years? It might be the last gasp of an expiring culture before we all get sucked into the [digital] cloud."

In the meantime, demand for vinyl shows no sign of letting up. Each year, around Record Store Day on the third Saturday of April, tempers flare over production runs, with bands and labels complaining they can't get their tracks pressed and accusing each other of sabotage. Production bottlenecks aside, it's significant that some of vinyl's big customers are now high-street stores. Moreover, vinyl's physical limitations – two sides, roughly 20 minutes each – is forcing a return to craft lost in an era of 70-minute CDs or single-track-focused iTunes sales. Chris Mara, at the analogue-only studio Welcome to 1979, says that artists still want to create music in terms of albums and they're prepared to step back in time to achieve that end.

Mara's side business repairing 24-track analogue tape machines has never been busier. "Bands come here because they want to record the hard way," says Mara. "They want to be able to say to themselves and their fans, this is our band. This is our craft. We played every note, in this spot."

Question is, can manufacturing keep up? Millar thinks it can – mothers, masters, plating-tanks, lacquers and all. "The revival happened and now we're shifting into higher gear. Vinyl's not going away. Maybe demand will plateau out at some point but that won't be about form, it'll be about content. For now, it's a pretty nice place to be."