The National, Brixton Academy, London

Peerless National treasures

"I guess I've always been a delicate man," Matt Berninger implored us, in those sumptuous baritone tones of his, on "Lemonworld". Well this "delicate" frontman is a serial stage diver, very fond of flinging himself – arms outstretched, wine (often red) bottle in hand – into the audience. Berninger did it earlier this year at the Royal Albert Hall; he memorably did it at the Royal Festival Hall last year. Here, in Brixton, he prowled the front of the stage, before succumbing and throwing himself in during the giddy "Mr November", near the set's end. It was a wholly apposite and joyous moment during a jubilant, deliciously indelicate gig.

After 11 years of being the best-kept secret in music, the Brooklyn-based, Ohio-raised five-piece, composed of Berninger and two sets of brothers, are out in the open. First they were uncovered by Barack Obama's rousing use of "Fake Empire" (from The National's fourth album, Boxer, and the soaring anthem induced a mass singalong here) during his 2008 election campaign. But, more crucially, they were exposed to the limelight by the release of their sensational High Violet, which opens with the distorted loveliness of "Terrible Love", with the pleading exhortation "It takes an ocean not to break". The album climbed as high as three in the US charts and bagged a Q award for Best Album.

The National have been threatening to produce a masterpiece since 2005's gorgeous, criminally undervalued Alligator, and the best of High Violet is performed in all its brooding, growling intensity here. It's indie-rock music redolent of REM, Leonard Cohen, Chris Isaak (which is a good thing), The Psychedelic Furs, but also reminiscent of a swathe of British post-punk bands from the Eighties – Joy Division, Echo and the Bunnymen (they reek of them), The Cure, Animals That Swim and, dare I say it, Big Country. The National's dark, affecting materials and their cryptic, sometimes baffling, always interesting lyrics have a cinematic quality. David Lynch's Mulholland Drive and Blue Velvet spring to mind, particularly on "Conversation 16", where Berninger wailed (he does a lot of wailing) "I was afraid I'd eat your brains/ because I'm evil". A hint of Bret Easton Ellis here, and the whole crowd, worryingly, joined in with "I'm evil"...

The Springsteen-like, saucy ("Lose our shirts in the fire tonight") "Runaway", omitted from the Albert Hall set, dizzily kicked off proceedings. However, they left out their exquisitely twisted "Karen" and their gorgeous, inscrutable anthem "Secret Meeting" (both from Alligator). It hardly mattered, though, as their new songs are so exquisite you don't pine for the "old" ones. Berninger applied his heady blend of growls, wails and pleas to "Sorrow", a lament with a whiff of teenage despair about it ("I don't want to get over you"), the unsettling "Afraid of Everyone", their single "Anyone's Ghost" and, best of all, "England", where he beseeched "Try to be nice, cos we're desperate to entertain."

They were desperate to entertain. They succeeded. Best album of the year. Best band, and gig, too. Lovely.