Watching Acid Klaus is often a surreal experience, toeing the line between pop perfection and all-out collapse. Tonight, however, is more surreal still. It's like the edge of the stage is a barrier between two universes. On one side is the most famous venue in the country, perhaps even the world, the imperial splendour of the Royal Albert Hall. On the other is Adrian Flanagan, stood behind a wooden stand on which 'Sexeh' is written in neon, and a half-drunk bottle of red wine is placed precariously next to his keyboard. A man of a thousand esoteric pop projects united only by his trademark bucket hat and shades – as well as his keen eye for a left-field banger – the strangeness of his presence in this building – "a gilded Arndale centre for posh people," as he calls it in his acid-tongued stage patter – is not lost on Flanagan himself, who responds by jabbing gleefully at the hall. "You look daft up there," he tells those sat in the fancy boxes. "Shush! I'm trying to concentrate!" he demands of his crowd when they dare to start talking between tracks.

Though the hall's only half full – most are still in the long queues to secure their £7.50 pints before headliner Róisín Murphy – those that are watching are brought on board by Flanagan's curmudgeonly charm. A few in the rafters even dare to dance. The music itself, it's worth pointing out, is brilliant. Flanagan and his stripped- back outfit – just him, mononymous drummer Dimitri and keyboard player Philly Piper – do not so much rise to their surroundings as bring their surroundings back down to their level. "I like to treat venues like I treat the Star And Garter in Manchester," says Flanagan after brief technical readjustments. They perform the same way you sense they might at four in the morning in a dingy lock-in, and that's what makes it great.

Flanagan is joined by a rotating cast of vocalists – Maria Uzor of Sink Ya Teeth combines intense energy with steely charisma; Cat Rin is magnetically manic on Welsh-language banger 'Bethlehem Or Bust'; Amsterdam's Lieselot Elzinga, also a fast-rising fashion designer, throws wild and angular shapes. Piper takes the mic for slick new single 'You're A Freak', and occasionally Flanagan does too, most notably for 'Bad Club Bad Drugs Bad People', for which he jumps straight through that imagined barrier and starts stalking the front rows like a morally inscrutable seaside entertainer. He chants the track's titular refrain – which feels more pointed than ever in these stuffy surroundings – as he tries to get a rise out of his crowd, at one stage by sitting on their laps and gyrating. Both a victory lap for a musician who's toiled away in music's outer reaches for decades with little mainstream reward, and a deeply bizarre experience for all involved, the collision of the two is most of all intensely fun.

Murphy, for whom the hall is now full to bursting, is far more at ease in such grand surroundings. As she did at her show-stealing West Holts headline slot at last year's Glastonbury Festival, she begins the show backstage, she and her band filmed on a phone and displayed on the stage's big screen in black and white as the grandiose spoken word that opens 'Simulation' – "I feel my story's still untold / But I'll make my own happy ending" – segues elegantly into the track's irresistible beat. Her charisma is such that she doesn't even have to be on stage to exert total control. The camera follows them as they walk towards the stage, slowly and deliberately to build maximum momentum, timing it so that when she eventually shows the room totally erupts. Every single person leaves their seat in joyous ovation and dance. Very few of them will return for the next two hours.

Murphy's not exactly short of hits, but it's a mark of her control over the room that she can move instantly into unreleased single 'Hurtz' without losing a shred of momentum. The track shows off her rich and soulful vocals to their fullest, but her sense of silliness is always present to puncture any pretension. She's all too happy to bust out an enthusiastic running man dance halfway through the evening's first big hit, her old band Moloko's 'The Time Is Now'. On another new track, 'Universe', which contains a nautical-themed monologue in an American accent, she delivers it with am-dram levels of ham. Her sense of glee is infectious, taking over the entirety of this old hall and erasing any trace of stuffiness. Costumes are changed frequently – from an elegant blue dress into an oversized gold jumpsuit, then into full-on technicolour dreamcoat and again into a shimmering southern belle ballgown. Hats and headpieces – some of them beautiful, others absurd – are rotated more frequently still.

After a slicked-back sequence including latest single 'CooCool', momentum starts to ease, that is until the set's centrepiece arrives in the form of 'Something More'. It starts slowly, the vocals a capella before the beat kicks in slowly and deliberately, rising in intensity until it morphs effortlessly into the sublime disco beat of 'Let Me Know'. From hereon out the gig's an all-out party. After more new material she unleashes Moloko's 'Sing It Back', and then another medley – this time the opening of 'Murphy's Law' flowing neatly into her recent DJ Koze collaboration 'Can't Replicate'. Having built up unbelievable momentum, she takes it plunging down into the demented clangs of 'Ramalama (Bang Bang)', and all the way back up again to the euphoric heights of 'Flash Of Light', after which she leaves the stage to scenes of absolute rhapsody.

Before an encore of material from her most complex and dynamic record, 2015's Hairless Toys, Murphy repeats her opening trick all over again. Once again filmed backstage and displayed onscreen, once more her band whirr gradually into motion. Once more they parade slowly and deliberately towards the stage, and once more there's an eruption of noise once they're in eyeshot. Afterwards they leave as they entered, Murphy singing the closing bars of 'Unputdownable' while closing the stage door slowly to the camera. Such is the joy still buzzing around the room, that she might easily re-emerge ten times over and still receive the same reception.