Nevertheless they are centre-stage tonight, under the auspices of Lord Eric Sugumugu, who founded this group of a dozen musicians in 1975, each player hailing from a different African country. The only non-percussionist in the ensemble is a lone oud player.
Still, things get off to a less than auspicious start. The opening water-pouring ritual loses something of its gravity when the water is poured from a South Bank Centre Styrofoam cup. And Lord Eric's unintentionally patronising explanations as to where our boat or plane has now landed, as we take our virtual journey around the noisy continent - Ghana, Congo, Ethiopia, Sudan and so on - tends to interrupt the flow of the music. But once the MDAs are at full tilt, these petty gripes are forgotten.
This music comes at you in waves, relentlessly. At its most thrilling, the experience is like being under a bridge while a very long goods train passes over it. At its subtlest, you can take pleasure in the amazing variety of tones and textures generated by African percussion instruments, and what they evoke. For example the Nigerian Yoruba drums - great, fat, cigar-shaped objects, almost as large as the men who beat them - sound like a rumble of distant thunder when hit lightly, but like a wardrobe being pushed over when hit with force. And what beautiful objects they are too; not a hum-drum snare in sight.
The most enjoyable excursions are "Kenya", a sultry blues where, for once, the oud player gets to be the focus of attention. And "Nigeria", when the roots of Fela's Afrobeat are movingly apparent. The momentum the drummers conjure makes it hard to imagine such a song ending. Its very point - its religious power - seems to reside in its endlessness. You relax into this awesome noise, becoming aware of riffs and musical motifs in the various timbres, just as, when you stare into darkness, vague shapes eventually turn themselves into familiar forms. The graceful sweep of the music becomes a parallel experience to the cacophony of the moment. By the encore - a new piece: "We are One" - the audience are on their feet and dancing.
Maybe, one day, our pop music will be more like this.