Multi-artist concerts can often become unwieldy, but this expertly programmed celebration of 75 years of the British Council crossed several cultural and musical boundaries with hardly a glitch.

It built nicely, starting with the relaxed Afro-blues supergroup of Justin Adams and Juldeh Camara, with Egyptian violinist Mohamed Medhat, ngoni virtuoso Bassekou Kouyate and honey-toned singer Amy Sacko.

Then, framed by video clips about the council's work, we had hypnotic Arabic/Celtic meditations from Kamilya Jubran, Karine Polwart and piper Fraser Fifield. The engagingly shambolic Guillemots clashed politely with Arthur Jeffes's second-generation Penguins, closing the first half with a twanging Telephone Rubber Band, a dramatic waltz and a lullaby.

The long second half belonged to Matthew Herbert's Big Band. After a fanfare, Herbert sidled to a table piled with electronics and, sampling and twisting the trumpets into a vinegary loop, kicked off The Story. Few artists combine politics, the avant garde and entertainment with Herbert's confidence, and his band has acquired a solid, hard-swinging ensemble sound without losing edge.

But Herbert had a couple more tricks up the sleeves of his tailcoat. There was the well-drilled Goldsmiths Vocal Ensemble, happy to dance, don hoods and do other business as well as sing. And singer Eska, in a comic-book costume – huge shoulder pads, sculpted hair and a glittering glove – turned a good gig into a great one. Whether finessing the arrangement of Just Swing or letting rip on The Yessness, she's a magnetic performer who can go over the top without losing musicality.

Herbert, by contrast, is half Buster Keaton, half Mark Thomas, and each song makes a point. One Life runs over a rapid blip track, sampled from the NHS incubator that saved Herbert's premature baby. Each blip represents 100 lives lost in Iraq between 2003 and October 2006.