The Venue is not the kind of place you’d expect to find a band with a gold-selling album, a slot on Glastonbury’s Pyramid stage and nominations for Ivor Novello and Brit awards. Coming attractions at the hall just off Derby’s inner ring road include the Craig Charles Funk & Soul Club and tribute band the Clone Roses. It is also available for parties and weddings. London quartet Wolf Alice are here to kick off a week-long tour of small venues, extending from Dundee to Guildford, to road-test their excellent second album, Visions of a Life. Thus their first ever show in Derby takes place in a venue they might easily have played on the way up, not so long ago.

On the face of it, Wolf Alice seem like a band who might have been cultivated in a secret laboratory beneath the BBC 6 Music studios, such is the sure-footed brio with which they deliver the core satisfactions of indie rock. They began in 2010 as a folk duo, comprising singer-guitarist Ellie Rowsell and guitarist Joff Oddie, before expanding into a four-piece in 2012 and building a fanbase through ceaseless touring. Listeners significantly older than the band members will be able to identify hints (but not pastiches) of countless groups from the pre-Britpop 90s, whether it’s PJ Harvey, Slowdive or Hole, so it’s no surprise that tonight’s audience includes both teenagers and the parents of teenagers. There is something quintessential about Wolf Alice, which might explain why director Michael Winterbottom chose them as the subject for his unorthodox tour documentary On the Road, and this small, friendly room, hot and clammy on a summer’s night, is a quintessential indie venue. With no disrespect to Derby, Rowsell’s lyrics about adolescent home town frustration — “What’s there to do in this dead old town?” (Fluffy), “Tired of waiting for the bus to nowhere” (Giant Peach) — hit harder here than they did at, say, New York’s Irving Plaza.

At this stage, Wolf Alice’s appeal is obvious, but to get this far they had to slash a path through thickets of thinkpieces about how guitar music was dead. It’s very easy for a four-piece rock band in 2017 to sound retro or ordinary; it takes great charisma and some knockout songwriting to make these components feel fresh and vital. Songs like Fluffy and Moaning Lisa Smile find the perfect ratio of melody to noise, with lyrics that sharply document the joys and anxieties of youth: the sweetness of childhood friendship on Bros, the paralysing claustrophobia of depression on Silk, predatory creeps on You’re a Germ. Bassist Theo Ellis politely asks fans to “watch through your eyes and not your phones” but most are too busy moving to take out their devices.

Predictably, the older songs incite the most frenzied pogoing and crowdsurfing but the new ones, played for the first time in Britain after a short US tour, are more impressive, expanding Wolf Alice’s sound in several directions. Their breadth hinges on Rowsell’s ability to assume different voices. It’s a long way from the dreamy quasi-rap of guitarless set opener Don’t Delete the Kisses to Yuk Foo’s hand grenade of riot grrrl rage, and thence to her arch precision on Formidable Cool’s roiling dance-rock. She can sigh like Hope Sandoval on Blush yet deliver the final word of Yuk Foo with a delicious Johnny Rotten flourish: “Shit-ah!” Most audacious of all is the new album’s eight-minute title track, which first glowers, then gallops, edging into the eldritch hard rock of Black Sabbath with thunderous salvoes from drummer Joel Amey. It takes a while to appreciate that each member is as confidently versatile as Rowsell.

Apart from a cheerful cry of “Derby, Derby, Derby!” Rowsell isn’t much of a talker, but she’s a mesmerising performer, relatable with a shard of enigma — or maybe shyness that reads as enigma. So it’s all the more thrilling when, during Giant Peach, the raucous conclusion to a taut, hour-long set, she launches herself into the crowd, stands atop a trellis of raised hands, and screams the closing lines into some startled, delighted faces. Band and audience both leave glowing with sweat. Wolf Alice will soon be returning to much bigger venues, but this back-to-their-roots detour was a visceral, intimate treat. It’s a shame Winterbottom’s camera missed this one.