British Sea Power, Regent's Park Open Air Theatre, London<br/>The XX, Hoxton Hall, London

It ended on a leafy stage. This much is certain. How we got to that dramatic denouement is lost in a blur of chaos and confusion. British Sea Power step out under a blood-red sky into a tree-ringed circus, its deciduous sentries guarding a steeply banked auditorium, pitched towards an Italianate villa which is more accustomed to putting on Romeo and Juliet than rock'n'roll bands.

The Big Wheel Sundays season rivals – and maybe surpasses – Somerset House's Summer Set for civilised and picturesque open-air gigging in the capital. For most bands, this would be the most unusual venue they'll ever play. For BSP, whose live schedule can include such stops as the Czech embassy, Britain's most elevated pub and the offshore fort of Sealand, it's among the more mundane.

They've risen to the thespian theme sartorially, singer Yan in Puckish plus-fours and stockings, his brother Hamilton in a crown of laurel leaves, violinist Abi Fry in her Roman robe looking like his wife Portia, and keyboardist Phil Sumner swilling rouge from the bottle like a Withnail-esque old soak. I can't see Wood for the hi-hats, but for all I know the drummer is blacked up as Othello.

They aren't alone. For much of the show, the twin staircases behind the Cumbrian band are occupied by the extraordinary London Bulgarian Choir in their traditional embroidered smocks, adding their ghostly voices to "Men Together Today", and gamely assisting the "Easy! Easy!" wrestling chant in "No Lucifer". British Sea Power aren't the first in the indie sector to discover the magic of ancient Bulgarian folk singing: in 1986, Ivo Watts-Russell, encouraged by Peter Murphy of Bauhaus, issued the Le Mystère des Voix Bulgares album on the 4AD label. But it's a timely rediscovery. Prior to BSP, the LBC belt out a set of their own, all diaphonics, dissonance and irregular rhythms, simultaneously haunting and hearty, eerie yet emphatic, and utterly bewitching.

The choir's presence proves that, far from the fogeyish Little Englanders the band's name and general demeanour might convey to the uninitiated, British Sea Power are actually proud grands Européens, and an ever-rousing "Waving Flags" is a hymn to pan-continental solidarity to a Joe Meek soundtrack. Indeed, in a month when we've lost Henry Allingham and Harry Patch, British Sea Power – whose early gigs had them wearing First World War uniform and taking the stage to the opening scene from A Matter of Life and Death – are one of only two bands I can think of who would know or care what it all meant.

British Sea Power – the History Boys of rock music – are the perfect synergy of the intellectual and the physical. Tonight we hear songs about Dostoyevsky and Charles Lindbergh, the splitting of the atom and the radioactive shadow of Windscale and the fear of mortality. But we also encounter music of such stirring visceral force that Regent's Park security doesn't know how to react to the frenzy, with the Third Battalion – BSP's hardcore fan squadron – brandishing branches like the advancing army in Macbeth.

"This is the rowdiest picnic I've ever been to," says guitarist Noble. "This isn't a Rolling Stones moment," Yan intervenes, "but people are getting hurt. Dance up and down, not side to side." But the real bedlam is yet to come. As the encore of "Carrion", "All in It" and "Rock in A", a giant 10ft bear dances through the aisles, thrashed with branches as he goes. (It transpires that the suit's occupant is Gavin & Stacey's Mathew Horne.) Meanwhile, Hamilton is shinning precariously up the central flagpole. Yan falls to his battered knees, pulls a rock-hero pose, and they're gone, Bulgars and all, and the only thing left is a whirl of leaves.

Shakespeare meets Schama, plugs into a Marshall amp and tears it up. British Sea Power ought to be compulsory on the curriculum.

It doesn't happen often, but I'll hold my hands up: I got it wrong. Last week, when I described the debut album by The XX as "wallpaper music", I hadn't given it enough time. A couple more listens, and it had grown into something else entirely. Yes, songs like "Basic Space" and "Crystalised" work as background mood music, but gradually their tendril-like arms reached out from the wallpaper, slowly enveloping me.

They're equally beguiling live. Shadowy figures on a shadowy stage in what is rapidly becoming my favourite new (or new-old) London venue, the quartet of 19-year-olds conjure an exquisite self-absorbed gloom, led by the elegantly intertwining vocals of Romy Madley Croft and Oliver Sim – a Serge & Jane from the dark side – with a restraint and subtlety beyond their tender years. It's the kind of music teenagers voraciously consume, as Robert Smith's bank manager can attest, but rarely create themselves. Or at least, never this well.