As frontman Adam Granduciel notes from the stage, 10 years ago the War on Drugs were playing a tiny room at London’s Corsica Studios nightclub. Now here they are: Grammy winners packing out the O2, an ascent no one would have bet on, even when the critics started screaming about the Philadelphia band’s 2014 album Lost in the Dream. They are no one’s idea of charismatic or visually prepossessing performers, and they’re strangers to the dark art of projecting your personality to row ZZ. Nor do they distract with attention-grabbing production: there are two video screens that exclusively show what’s happening on stage, an understated light show, and that’s it. Yet musically their ascent into what musicians called “the sheds” makes a weird kind of sense. Their songs recall a strain of 80s Big Rock, most obviously Bruce Springsteen – a similarity bolstered by the presence of a baritone sax – but also the lengthy extemporisations of Dire Straits’ live album Alchemy, the hip dad’s car stereo companion of choice circa 1984. At the other extreme, they evoke the taut rhythms and electronic exploration of Krautrock, their devotion to the sound of 70s West Germany enshrined in the title of Harmonia’s Dream. It’s a combination that looks ridiculous on paper, but works so well live you wonder why no one thought of it sooner. The melodies roar anthemically, topped off with air-punch-inducing valedictory synth lines, building up to lengthy finales decked out with pyrotechnic guitar solos. The motorik beats drive everything relentlessly along, and the electronic intros and interludes – frequently extended live – provide teasing, anticipatory dynamic shifts and pleasingly WTF? moments. It’s hard not to be struck by the weirdness of the fact that you’re sitting in London’s biggest indoor venue listening to a band who at that moment sound remarkably like kosmische experimentalists Cluster. That there’s something for everyone here is reflected in the audience, which ranges from twentysomething hipsters to men old enough to remember the day Mark Knopfler first donned his headband. The improbability of their sonic cocktail leads to moments when the usual logic of arena rock is turned on its head. During a rapturously received Under the Pressure, the music shifts into a lower, beatless gear. A spotlight picks out drummer Charlie Hall and the audience whoop in time-honoured style. But Hall doesn’t play a solo. He just hammers metronomically at his hi-hat. Then the song surges into life again, struggling to be heard over the crowd’s roar.