When south Londoner Eska Mtungwazi released her first album as a frontline artist, after 10 years as a backing vocalist to names such as Grace Jones and Matthew Herbert, things happened quickly. Near-unanimous praise for her self-titled debut was followed by a nomination for this year’s Mercury prize. She didn’t win, but playing a sold-out tour a week after the ceremony probably offers some consolation.

Eska enters, statuesque and imperious, several minutes after her band signal their own arrival with the clunk of a cowbell. Her iciness swiftly dissolves into good-vibe benevolence; as a free-flowing introductory amble ends with Heroes and Villains’s Brit-reggae shuffle, it’s evident that success has only magnified her amiable accessibility. Though tonight’s dozen-plus songs are often about indomitability, the singer cloaks it in references to her favourite hymn, Rock of Ages (“it’s about gentleness, and gentleness brought us here”), and a goofball cover of Devo’s version of (I Can’t Get No) Satisfaction. Her voice, astringent at the top and rich at the bottom, could have turned Satisfaction into booming karaoke, but she stays true to Devo’s whiny frustration.

Untethered to any genre, she drifts from Pentangle-y psych-folk on She’s in the Flowers to Arrogant Heart’s desolate blues, the latter’s spookiness emphasised by the cuatro (bass ukulele) she plucks. There’s an interlude where she steps back and lets the band do their uptown-funky worst, as she bangs a tambourine and swings her braids around her head; it’s followed by a harmonica solo by Philip Achille that briefly threatens to eclipse everything else we’ve heard tonight.

But nobody puts Eska in a corner. The venue’s 1930s municipal grandeur may be the wrong setting for her open-hearted eclecticism and her band sometimes noodle as if they’re backing Sting circa The Dream of the Blue Turtles, yet Mtungwazi comes out on top, strong and remarkable throughout.