Alabaster dePlume does not know what he is doing. He says as much near the start of his set.

“I know I’m supposed to behave like I know what I’m doing,” the saxophonist, singer, performance poet and bandleader adds, before proceeding to harmonise with the sound of a distant toilet hand-dryer. Later, he will conduct his band in a cappella vocals with a fingerless-gloved hand, pointing at the notes in the air, and repeatedly congratulate his audience for being alive.

Born Gus Fairbairn 41 years ago in Manchester, but now based in London, dePlume talks – and sings – effusively about the very act of performing even as he is performing, interrogating himself and the role of performer as he goes. At one point, he introduces a new song, Oh My Actual Days. He runs the band, and the audience, through how it should go. “If it doesn’t,” he says, with the wild-eyed intensity of a cult leader, “YES!”

The track begins as many of the best DePlume tracks do: simply, as a pensive sax motif. The rest of the band – tonight, two drummers, a bassist, an electric guitarist and a synth player, a 50/50 split of genders – find their way in, with backing vocalist and percussionist Donna Thompson, singing guitarist Marcelo Frota and vocalising drummer Momoko Gill picking up the wordless refrain, at once sad and sultry. “Stay!” commands DePlume. And while the band remain in a holding pattern, his saxophone line goes off alone until the whole ersatz public rehearsal resolves, quite beautifully.

DePlume has been working at the cusp of improvisational collaboration and what you might call “spoken word with instruments” for some years now. But his last two albums, both released on the respected US avant-jazz label International Anthem, have marked a contextual step up in DePlume’s complex offering, and his name recognition.

To Cy & Lee: Instrumentals Vol 1 (2020) compiled a series of stately, immersive compositions dedicated to two of the adults with learning disabilities with whom Fairbairn worked for some years in Manchester. Many of these instrumentals (often previously released on the Lost Map label) found his sinuous saxophone and a host of guest musicians concocting a kind of abstract, ambient, spiritual-leaning jazz, brimming with emotion.

Tonight, DePlume’s reed-playing, side-on to the microphone, feels fresh, non-canonical and instinctive. (He is quite happy to tell interviewers that he got into jazz through the soundtrack to the Japanese anime Cowboy Bebop.) Anyone into the Éthiopiques compilations of vintage east African jazz will find much to swoon over in his tone, in the sumptuous, heady loveliness of his internal weather.

And yet when the pace picks up, his staccato phrasing recalls the rousing blare of Shabaka Hutchings, an associate and collaborator from north-east London’s Total Refreshment Centre, one of the centres of the last decade of the fertile London scene. Tonight, the heady dub skronk of the set’s climax, Broken Like, finds the previously seated bassist Rosetta Carr on her feet, leading the judder on this angry-party-jazz workout.

But there is the other side to DePlume. He’s a garrulous, heart-on-sleeve rabble-rouser, an anti-cynic keen to reduce the fourth wall to rubble. His album of last April, Gold: Go Forth In the Courage of Your Love, was also ecstatically received. It returned the focus back to DePlume’s previous, more declamatory style, in which personal and political themes trade off as a dizzying array of collaborators thrum beneath.

Live, he is both combative and full of delight; holding forth in a way that melds traditions, like Scottish poet Ivor Cutler or the Fall’s Mark E Smith declaiming the works of Gil Scott-Heron at a cost of living protest. The tone is unmistakably 2022. “I was gonna fight fascism,” goes another of DePlume’s more frontline works, a diatribe against complacency he originally recorded with the band Soccer96. It lists a lot of understandable, but ultimately feeble reasons why one might not act on one’s principles. (“I had a lot on,” goes one line; it’s important to note that DePlume is castigating himself, as much as anyone else.)

Tonight, the track is reworked for laughs – but also, not for laughs. “I was gonna fight fascism,” yells DePlume, “but I was really angry with all the other people who were fighting fascism in the wrong ways, so I went on Facebook instead!” All this goes hand in hand with a flurry of supportive affirmations. Don’t wait for permission to unleash your own special gifts on the world, he urges.

Don’t Forget You’re Precious is Gold’s totem tune, an exhortation to remember that human beings are delicate. It doubles as a plea for unity in the face of division. Because, DePlume notes, there is a lot of effort being put into stoking division. “We’re gonna need each other for what’s coming,” he says, with a haunted look. “And I don’t mean my last song.”