Tony Allen with the Hypnotic Brass Ensemble

The crowd is packed in so tight that dancing isn’t an option. Despite the disparate star guests – Natty, Damon Albarn and Baaba Maal – they are almost all here for Chicago’s obscure nine-piece jazz band the Hypnotic Brass Ensemble. Eight of these slickly hip-hop-styled young men are sons of Phil Cohran, trumpeter in Sun Ra’s space-jazz Arkestra and founder of the Association for the Advancement of Creative Musicians.

This passionate advocate of avant-garde jazz must have despaired as he saw the music marginalised in America. His children’s stated dream is to reclaim the respect rappers are shown for musicians, to recover Chicago’s golden early 1970s groove, when Curtis Mayfield’s symphonic soul ruled the streets. Modern guerrilla marketing, playing in public places with the results put on to YouTube, has helped. Their fans call for favourite instrumentals, as jazz returns to its roots as tough dance music, taking all tonight’s performers with it.

This is equally true when Allen is on stage. The great Nigerian drummer who forged Afrobeat with Fela Kuti in the1970s justifiably takes top billing, in this gig in Cargo’s Broad Casting collaborative series. He plays tag between his own quartet and the Ensemble. His crew are funkier, showing up the latter’s lack of swing, and lack of interest in the melancholy introspection of a Miles Davis. Instead they use brass, backed by drums, for pure percussive attack. Allen himself is, as always, a study in economy. Arms low and close to the body, he holds one drum-stick at times like a child clumsily clutching a pencil, yet flicks out inquisitive rhythms that roll through the night.

London rapper Ty adds a gruff vocal layer. Natty, currently the biggest British reggae star, tries a transported, incantatory mode, whispering, “don’t believe what they say.” Then Maal takes two songs to blow everyone else away. “I feel like I’m in Lagos,” he smiles, hearing Allen. His excited eyes, tense energy and soaring voice force the most thrilling brass blast of the night.

Albarn croons a downbeat spiritual song on the edge of off-key, retuning the Ensemble to an Arabic style. He is booed by some of a crowd here to dance. But as Allen and the Ensemble play past midnight, the musically open cross-fertilisations of which Albarn is so often a linchpin are gathering pace.