First Night: Arctic Monkeys, O2 Academy, Brixton, London

Arctic Monkeys played their first UK show in two years last night with an ease confirming their special status. With Blur seemingly re-retired, and Radiohead these days floating above normal rock rules of engagement, they are the most respected UK band still standing.

Barely three years ago, they were either dismissed as a MySpace-bred fad, or praised as chroniclers of their Sheffield hometown's seedy but vibrant life. They recovered from that fame's early shock to become a remarkably dextrous rock band. Their singer-songwriter Alex Turner, too, always a cool-eyed observer of street-life, wasn't phased by no longer living it.

Second album Favourite Worst Nightmare and his subsequent side-project Last Shadow Puppets smoothly moved into moodier, more mysterious terrain. New album Humbug, partly recorded with Queens of the Stone Age's Josh Homme as producer, has been wrongly typed as a switch to harder, more American rock. In fact it's a continuing evolution into pop and lyrical classicism, where Hendrix meets forgotten Yorkshire folk satirist Jake Thackray as influences, in an elegant 21st-century version of Cream's "White Room". It's a long but steady course from the "mardy bums" and "scummy men" of their street-wise debut; progress maintained tonight.

A dramatically sudden entrance soon leads into Nick Cave's "Red Right Hand", the diabolic fantasies of which are playfully approached. You'd never mistake the floppy-haired Turner, in his smart-casual short-sleeved shirt, for Nick Cave, much less Old Nick. Any demons he has stay private. It's his calmness on stage, his lack of star presence or messianic pretension, which keeps his band usefully anonymous. Even his relationship with the glamorous TV presenter Alexa Chung can't draw the paparazzi's glare. When he shakes his long locks as he cuts loose on guitar, it's a shock.

It's left to the exact dynamics, thunderous riffs and tumbledown energy of the songs to purge his and the crowd's frustrations. Reversing through the three Arctics albums with "Crying Lightning", "Brianstorm" and "Still Take You Home", breathless precision unites them. Breakthrough hit "I Bet You Look Good On the Dancefloor" is sung by the crowd and seized as their own, lost in its precocious lyrics, and a riff tough and tight enough to kick-start a career.

The dusty psychedelic expansiveness of at least one new song, "Dangerous Animals", bares the influence of Josh Homme's American desert-rock. In a set boldly dominated by Humbug – only heard by most here since its Monday release – "The View From the Afternoon", from their debut, is then greeted with relief. I too start to miss the precise, humane observation Turner mostly veils these days. As if in answer, Humbug's best song "Cornerstone" follows, exuding all the old storytelling warmth. Then there's the Hawaiian guitar of "Only Ones Who Know", and cinema-style organ in "Fluorescent Adolescent" which might have closed a Mecca ballroom in 1962, and the Arctic Monkeys have re-found their balance: a mixture of The Shadows, Pulp and Pearl Jam, made in Sheffield, but increasingly beyond time and place.