Loyle Carner has his stage set out like that of a play – or perhaps it’s a family living room. A leather armchair sits stage-right while a bookcase stuffed with old vinyl becomes a deck for the superb beatmaker Rebel Kleff.

The crowd are on their feet within seconds of the 21-year-old’s arrival onstage, as he begins a seamless run through tracks off his debut album Yesterday’s Gone.

That hazy, mellow rhythm of “Mean It In The Morning”, interspersed with that simple “clack” of a drum beat, is so strongly reminiscent of the pacing and tone on Mos Def’s “Auditorum”, particularly when Carner actually gives him a shout-out on the track; the vibe continues on “Damselfly” that brings Tom Misch to the stage with his guitar, evoking the short sweetness of summer days.

Offering up beautiful vignettes of life at home with his friends and family, Carner worries about texts from girls along with anxieties about money, work and responsibility while his friends are out having fun; upping the tempo on a few of his more mellow tracks to keep the energy flowing.

He pours warmth and soul into tracks like “Florence” where he imagines life with a babysister, “Mrs C” – his spoken-word piece dedicated to a friend and her mother – and the gorgeous “Sun of Jean”, starring a spoken-word performance from his mother, who beams down at him proudly from her seat in the audience.

Like his heroes – Jehst, Mos Def, Nas, Common, Benjamin Zephaniah – Carner has an astonishing ability to evoke the world that surrounds him, and he also shares their capacity for storytelling. We get a perfect balance between the influences he draws on from the best of US hip hop and the power of his own, distinctly south London voice that spits out a superb freestyle halfway through his set.

The gospel chant on “The Isle of Arran” that recalls “California Dreamin’”; the funk-driven guitar riff on “NO CD” and the bluesy sax on “Ain't Nothing Changed” – all of this is testament to Carner’s understanding of how important the sample is for hip hop.

“Oi, no moshing,” he chides the front row gently when they become a little too rowdy, then, with a sense of fun and mischief that recalls French rap duo Casseurs Flowters, he can’t repress a grin as his hero Jehst arrives onstage and Kleff moves away from his deck for a storming rendition of “No Worries”.

Later, as a still-standing crowd scream for more, he flops down on the floor with an expression of touching disbelief plastered across his face, gets up again and bounds off in a daze, as the emotional album closer “Yesterday’s Gone” plays out.

It’s a rare thing to watch a performance from such a new talent and still be thinking about it well into the next day, but that’s Loyle Carner – and the thrill of watching an artist on the cusp of something big.