King Creosote & Jon Hopkins, Queen Elizabeth Hall

There are some acts you’d rather not catch in a concert hall. The relatively recent pairing of King Creosote and Jon Hopkins isn’t, however, one of them. Diamond Mine, their seven-year project, is a deceptively serious piece of art that prefers to be listened to closely and without distraction. It may have been one of the more obscure nominees at this year’s Mercury Prize, but that recognition has resulted in an album that could easily have slipped quietly by, gaining fans fast. And last night those fans found themselves immersed in Diamond Mine’s meditative soundscapes whilst, on stage, one eccentric and one prodigy gave a masterful demonstration of the benefits of perseverance.

King Creosote, AKA Kenny Anderson, has never been one to do things the conventional way. Yet even by his standards, Diamond Mine is an oddball concept. It came about over nights out with producer friend Hopkins. At the end of these evenings Hopkins got to thinking. At home he searched through Anderson's 40-album back catalogue, and when he’d found songs ripe for reimagining, he went up to the Scottish folk singer’s home, near Fife. He also brought his digital recorder, recording the little ambient sounds that convey lives lived; the clatter of cups in cafés, seagulls going by and bicycles freewheeling. Then he brought Anderson down to London to record new vocals.

The result has been what they call a “soundscape to the lives of an imaginary Scottish fishing village”. But it’s more than that. Both gentle and desperate, it captures the longings and sorrows of everyday lives in a way that can reduce you to tears. The atmosphere in the Queen Elizabeth Hall might not have been quite so palpably emotional but still the audience's attention was still rapt.

Warmed up by a mix of avant-garde, indie and French art-house from support Frànçois and the Atlas Mountains, after the interval the room had reached a level of relaxed seriousness perfect for appreciating an album that's best described simply as contemporary music. It may have been being sung by a small, hairy folk singer, but it was every bit as valid as a piece of serious concert music as anything by Steve Reich.

And like Reich, things kicked off with tapes and those café scenes that open the album. With the pin-drop clarity of the hall’s acoustics, these were as evocative as on record. The evening, however, really belonged to Anderson’s singing. Wearing a scruffy check shirt and grasping a bottle of brown ale, he shuffled on looking like a roadie. The tall angular Hopkins sat at his right behind a grand piano and a baffling box of electronics. To his left was a girl who looked a bit like Janine from This is Spinal Tap, and to her left a violin and viola player. In front, coming out of Anderson’s mouth was just the most mesmerising sound.

Lyrically, the songs from Diamond Mine worked a bit like Radiohead's. You were less inclined to listen to the words all the way through. But it was lines and fragments, along with the plaintive delivery and haunting chords, that stuck with you. In "John Taylor’s Month Away", the protagonist saw lonely sailors eyeing up girls that they couldn’t afford and repeated, “For once in my life, I’d rather be me”, the middle-aged man in “Bats in the Attic” saw “silver in his sideburns” and was “starting to unravel”, while the sadness in the lines “It’s your young voice that keeps me hanging on/ To my dull life” (“Your Young Voice”) was redeemed by the love behind it.

And instead of the conventional strum of a guitar, these extraordinary songs hung on sustained piano chords, electronic pulses and pizzicato strings. Hopkins's triumph was one of taste, knowing exactly what to put where, and never being tempted to put in too much.

The album, played in its short 32-minute entirety, was then followed by another half-hour of songs by Creosote. Of these, two - “And the Racket They Made” and “Leslie” - were arranged similarly to Diamond Mine. “Spystick” was so strong that, although it wasn’t, you could easily imagine it pushed or pulled any way you liked. However, it was “Cockle Shell” with its interweaving guitar and piano parts that everyone was going to remember the next day.

Anderson is said to have spent most of this year bemused that after 40 albums, and collaborations such as The Burns Unit, he’s come across a way of presenting his music that takes him beyond the folk clubs. But after Diamond Mine, the question presents itself of whether the formula is good for a second album. The second half of last night’s concert said emphatically, yes. And apparently, a new EP has been cut. Look out for Honest Words on 19 September.

• Find King Creosote and Jon Hopkins on Amazon
• Download King Creosote on iTunes
• Book tickets for King Creosote on tour in October and November

Creosote and Hopkins perform "Bubble"