The further we get from the 20th century, the harder it becomes to account for the appeal of amplified guitar music. The cultural moment has moved on, but a genre that can sometimes feel like some throwback to a more priapic, unenlightened time can still provide thrills and succour in equal measure.

Bands like the Raconteurs exist, in some part, to remind everyone of the allure of being pinned to the back wall by analogue sound, of the fun in being shaken up like microplastics in a snow globe by a riff. Starring Jack White (the White Stripes, the Dead Weather, his solo career, the Seven Nation Army riff terrace chant, Grammies) but meaningfully co-fronted by singer-songwriter Brendan Benson (six underrated solo albums, own record label, writer-producer for hire), the Raconteurs will, next month, release their first album in over a decade. It is “some rock’n’roll that you’ve been waiting to hear!” according to White – in carnival-barker mode tonight under incandescent orange lights. We’re instructed to tell our brother’s grandma. White, a retromaniac, carries off this shtick well, with one foot knowingly planted in a time when rock’n’roll was shaping up to be a form synonymous with the triumph of western democracy.

Both men stand on the monitors: Benson, rangy to the point of undernourishment, and White, clearly having a ball

If that time seems long ago, then this recently reanimated band still feel relevant and energised, after a decade’s hiatus. Tonight’s gig is an “undersell” – an intimate sell-out show, well below the numbers they could shift – in what Benson drily calls “a proper rock’n’roll venue”. The band are in town for the All Points East festival in London at the weekend.

The four core Raconteurs (plus one touring member), might be all male and no longer young, but they can still draw in the guitar-curious of all ages. One new song, Help Me, Stranger, the almost-title track of their third album, Help Us, Stranger, hymns the instrument. “If you call me I’ll come running,” sings Benson, “And you can call me anytime, these 16 strings we’re strumming, they will back up every line.”

Tonight, the total string-count can be up to 18, with touring member Dean Fertita chiming in on a third electric guitar, when he’s not playing keyboard or rattling a tambourine. At the set’s most messy point – that’ll be the awesome dub deconstruction of Steady, As She Goes, the band’s debut single – it’s as though White and Benson have inserted their twin lead guitars into the audience like egg beaters and pulsed the crowd to stiff peaks.

Both men, at one point or another, stand on the monitors: Benson, rangy to the point of undernourishment, and White, clearly having a ball. At one point in the Raconteurs’ early period the two had similar shaggy haircuts and presented as negatives of one another, one blond, one black-haired; it was purposely hard to tell who was singing on the record, and which songwriter had brought which song to the table.

Facebook Twitter Pinterest ‘Aggressive glam-stomp played at several speeds’: Jack White of the Raconteurs. Photograph: Richard Saker for the Observer

But since Consolers of the Lonely, the band’s second album from 2008, that stricture loosened up and you could see and hear the joins. So it is tonight, with Benson largely bringing the Beatle-y middle eights and bittersweetness, and White performing a slightly dialled-back version of “peak White”, the axe-wielding showboater.

Sometimes, White grandstands, as on You Don’t Understand Me, where his piano-playing glows as yellow as the lights. But the two men don’t look for confrontation in this all-guys-together set-up. When both are playing electric guitar, they can hand the melody back and forth between them on songs like the thrillingly nasty Top Yourself. On Old Enough, they interlock Benson’s acoustic with White’s electric. Duelling is beside the point.

Their new songs sit proudly among the heritage tracks. Bored and Razed comes early – its jazzy introductory circular riff giving way to a garage-rock party tune. Both men now live in Nashville, but were, to some extent, “Detroit born and raised”, as the tune has it.

Midway through, Don’t Bother Me is a sulky, passive-aggressive glam stomp played at several speeds, from Beatle to metal, by a well-oiled outfit who can step on the gas, and then, with a wave of White’s hand, come to a pregnant pause. “Your clicking and swiping don’t bother me,” sneers White. No, they can’t: our phones are locked away in Faraday pouches for the duration of the show. Everyone seems genuinely in the moment, not trying to see past a sea of screens.

Last year, White released a solo album, Boarding House Reach. Audiologically enthralling, it was, perhaps, a little difficult to love. Since then, his record label and cottage industry, Third Man, celebrated its 10th anniversary. Last month, he was awarded an honorary doctorate from Michigan’s Wayne State University, where he attended film classes in the 90s before leaving to pursue the White Stripes full time.

With Benson, and the ace rhythm section of Jack Lawrence and Patrick Keeler (long-time White henchmen), the Raconteurs have made an album of what are, relatively, straight-up bangers: an antidote of sorts to the bumpiness of Boarding House Reach. It actually reaches out: the cover shows a green pedestrian crossing light hand waiting to be taken. Keeler’s drumkit has a drawing of a hand with palm-reading lines across it.

And while it’s typically perverse of White to lace his marquee solo undertaking with difficult tunes, and his offshoot with tune after tune, this third Raconteurs outing is a blast. There is, though, a subplot of help, need and succour borne out by the lyrics. “Help me, stranger, help me get her off my mind,” the album goes.

And the album’s greatest hit is not audibly one of White’s contributions, but Benson’s magnificent Now That You’re Gone, a love-gone-wrong song that showcases his classic songwriter chops. White is on a Flying V guitar, leading a bit of a meaty clap-along, but Benson is at the eye of the storm with a deceptively simple song. “What will you do, now that you’re gone?” he asks, not a little passive-aggressively. As the taut verses and easy chorus play out, the lyric flips over to despair: “What will I do, now that you’re gone?