Klanghaus: On Air began life in an old animal hospital in Edinburgh two summers ago. Now, it's arrived at the Royal Festival Hall, and offers a thrilling, sonic trip through a normally hidden roof space of that great brutalist building.

Round a corner, and you never quite know what might be coming. So it's appropriate that the experience kicks off with a man in an echoey blue stairwell, singing hauntingly that infamous Donald Rumsfeld quote: "there are known knowns; there are things we know we know. We also know there are known unknowns; we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know."

Now, the American politician may have been referring to the contested existence of Weapons of Mass Destruction in Iraq, but that's about as topical as the night gets. This is not political theatre – it's not even really theatre. KlangHaus: On Air is more a gig than a play, albeit an incredibly inventively staged one. There is no story, plot or character; instead, Norwich band The Neutrinos rock out in and around the audience.

Still, the building itself almost feels like a character: this roof space is warm and dim, full of heavy metal machines, tempting levers, great big shiny air vents. It's a treat for curious snoops, and hums with atmosphere.

Their appropriately industrial noise rock fits the venue; drums, guitar and bass pound the ears and The Neutrinos' songs often have visceral, gutsy lyrics. More melancholic, mournful moments recall the sparse beats and smoked vocals of Portishead or Goldfrapp, with Karen Reilly making for a bewitchingly impish frontwoman.

But KlangHaus is almost as much about light as sound. The unusual space is used by their collaborator, artist and designer Sal Pittman, as a kind of canvas for projected light-effects, films and images of skies and water, which glide or gush across the walls and ceilings around the crowd and the band. The effect is like being inside a particularly cool music video.

Not that you'd have filmed this crowd: polite, static, attentive but pretty unresponsive given a guitar is being shredded right in front of them, or a woman is singing at their shoulder. Feeling wholly swept up, I found this awkward art-gallery reverence in the face of physically stimulating rock music slightly odd, almost hoping for a mosh pit to break out - but I guess that wouldn't have passed health and safety regulations…

What KlangHaus does very effectively create, however, is both a sense of brooding space - in the distance, you see projected wind turbines and jet engines - and real intimacy. While a lot of the music is loud (earplugs are available), at other moments, we gather round together on benches for low, finger-picked folk ditties. There's a magic to it.

Finally, from the warm, close, industrial space we're led up onto the Southbank Centre's roof – out, into the air, on air - for a view of the city at dusk. Flags emblazoned with the word ‘Love' are fluttering over the grey concrete as it stretches away and London begins to light up. It's a simple but gorgeously effective conclusion.

Klanghaus: On Air runs at the Southbank Centre as part of Festival of Love until 29 July.