The Low Anthem, Queen Elizabeth Hall, Londo

We're only two songs in at the Queen Elizabeth Hall and already ill winds are blowing through a very delicate musical landscape. Ben Knox Miller, the lead singer and bandleader, is a mite displeased. "How come all your cameras," he swipes at the photographers crouching in front of the stage, capturing the last moments of the barely-there "Ticket Taker", "which I know are digital, still make a fake shutter sound?" Oops. Shush, everyone. It's The Low Anthem.

It's a mark of how little it takes to nudge the pin-drop Americana of this band out of line; but unfortunately for Knox Miller and the rest of his Rhode Island gang, things are about to get worse before they get better – and then, thankfully, better and better still. It all begins beautifully – a tone set by a wonderful, bouncy opening salvo from Seattle's The Head and the Heart, perhaps the first band in history to be roundly forgiven for singing harmonies with their fingers stuck in their ears – as the foursome gather in a family circle for the plaintive "Ghost Woman Blues", mostly letting their voices do the work, although throughout the evening they swap and change instruments and then pick up even stranger ones – a musical saw, a flugelhorn – as a matter of course.

But then, just as the band hit their stride, from somewhere over near the pump organ – yes, the pump organ – the sound crackles, splutters and dies. It can be a very serious thing, this new Americana, and very earnest, too, and you can't help but cringe for the poor grafters wrestling with the electrics – but for The Low Anthem, it provides an opportunity to show a little warmth. They head up the steps into the heart of the auditorium – Jeff Prystowsky trailing behind a little under the weight of his double bass – and in the half-light, busk a wonderful mini-set of rousing folk songs. They each take a turn at a verse of Dominic Behan's setting of his brother Brendan's "The Auld Triangle" and rampage with exquisite abandon through Ramblin' Jack Elliott's "Cigarettes, Whiskey and Wild, Wild Women".

Here, and elsewhere tonight, particularly on songs from the band's latest album, Smart Flesh ("Apothecary Love", "Smart Flesh"), Knox Miller sounds more than a little like Dylan – but in truth the resonances echo far more fitfully about Dylan's great mentor, the Dust Bowl Troubadour himself, Woody Guthrie. There's something distinctly Depression-era about the aching desolation and the sad-eyed characters that drift through The Low Anthem's songs – and up into the rafters of the Queen Elizabeth Hall.

Back, finally, on stage, and almost perceptibly blinking in the light, the band plug in for a couple of gleefully discordant foot-stompers ("Boeing 737", "Hey, All You Hippies!") and wring substantial beauty from "This God Damn House", a song left as a parting gift, along with his house keys, by former bandmate Daniel Lefkowitz. Jocie Adams, not for the first time, extends herself on tip-toe and coaxes long, keening notes from her clarinet.

"Thanks for sticking with us," says Knox Miller as the last wisps of The Low Anthem's ethereal calling card, "Charlie Darwin", disintegrate. "It's been a strange night."