The Hives, Academy / Brixton Academy, Birmingham / London

They may be the hottest ticket in the country right now, but, Howlin' Pelle Almqvist's ego apart, the Hives have not been afflicted by a sense of gigantism. The Swedish band's home-made sign – which puts their name up in lights, floating over the widest stage in London like some kind of DIY UFO – has been replaced with a new, non-flammable version, but it's no bigger than the original.

It's apt, too. Though the motormouthed Almqvist relishes the chance to rampage through a stage set straight out of Elvis Presley's 1968 "Comeback Special", the rise to fame of a garage-rock band who make no concessions to musical fashion, dress in clearly home-made, matching outfits and display more imagination than budget in their videos has been sudden enough to outpace any over-ambitious stage concepts.

They remain five men with guitars, thrashing out the most reductive music imaginable. There are no guitar solos and hardly any melodies, just an infectious self-belief and an understanding of the art of showmanship. Almqvist's between-song boasts are treated with due respect – laughter and cheers. In London, he announces that he's a supporter of the concept of monarchy, before declaring himself the King of England. We've had plenty of Germans, so why not a Swede?

There's never been a better time to hail from the Scandinavian country. Before Sven restored the fortunes of the national football team, who could have imagined 3,000 Brummies at a rock show chanting, "Sweden, Sweden", in a call for the encore of "Hate to Say I Told You So"? A British or American band couldn't get away with such arrogance, no matter how witty they might be.

But the Hives are small-town lads who've invented their own mythology to escape the stifling surroundings of Fagersta, a place not very near anywhere. The drummer, Chris Grahn, became Chris Dangerous, while the guitarist, Micke Carlstroem, became Vigilante. They've even invented a Svengali figure, "Randy Fitzsimmons", although Almqvist introduces his elder brother, Nicholaus Arson, as Fitzsimmons in Birmingham.

New myths have already emerged. They're a figment of Bill "KLF" Drummond's imagination. They learn new moves at home to surprise their band-mates. Best of all, they were formed by two schoolteachers who took the likeliest lad and coached him into the rock'n'roll hero you see today (who started that one?).

They play at being a band 24/7. Turning up at your London after-show party in T-shirts emblazoned with your rock name is ridiculous, if explicable. Wearing said shirts in a Midlands dressing-room with half a dozen hangers-on present is true method acting. Persuading your girlfriends to sport shirts that read "Carlstroem" and "Destruction" blurs the lines completely.

The crowd get the gag: plenty of teenagers are wearing black shirts and white ties. Even the bear-like Ebbot Lundberg of the Soundtrack of Our Lives, the Brixton support act, sports said neckwear over his kaftan. They clearly adore the Hives for their frenetic performance and Almqvist's quick wit, something Doves and Black Rebel Motorcycle Club do not offer, whatever their virtues.

With a quarter of a million albums sold, then – and to a mixed audience – they've cracked it. Cynics might say that their fabulous punkomime is going nowhere in the long run, but that's like criticising a motorbike race for having no function as transport. Rock'n'roll's still not dead.