Toumani Diabate, St Luke's, London

With this concert at St Luke's, Toumani Diabaté left us in no doubt that two decades after recording his first solo album, Kaira, in London when he was just 20 years old, he has grown into a musician of world stature working at the height of his powers.

The Mande Variations – the reference to Bach is deliberate – is his second work for solo kora, recorded last year in London over a handful of sessions, and released without editing or overdubs. Straight from the hand to the ears, like the result of some purification process.

Praise must go to producer Nick Gold and engineer Jerry Boys for the quality of the kora's amplified sound both on record and in the concert hall – without the nest of carefully placed microphones around the great bulb of his instrument, you would be hard-pressed to hear it beyond the confines of a small room, let alone in the vaulting, red-brick interior of St Luke's.

Expectations are high and, over the next 90 minutes or so, they are fulfilled as we are treated to Diabaté's in-the-moment unravelling of The Mande Variations, whose improvised themes are drawn from the Malian folk tradition that stretches back at least to the 13th century. "This is not music that is written," he tells us at the close of the second song. "It is divine inspiration, which comes to my hand and heart and goes straight to the strings. We don't need to read music to play, you have to know that this music is older than A, B, C, D, it's older than classical music, than Bach and Mozart."

He begins with a new version of "Kaira", which opens with the sparest of melodic lines, soon underpinned by first one bass figure, then another, running together under an intensely lyrical lead while his fingers conjure up supporting rhythms that expand and contract with lives of their own. Where your jaw drops is down to you, but drop it will. And all the while he's tacking to the simple, unadorned melody he started with.

In the heart of the set is an improvisation, a strikingly modernist, free-form piece, ranging from an almost flamenco attack to fluid and spacious musical invention, Diabaté's head bobbing furiously to his own time signatures. From somewhere within it, a blues structure appears like a mirage, before shimmering and fading back into the root melody.

The following "Cantelowes" has its The Good, the Bad and the Ugly theme as an opening statement, which provokes laughs of recognition that fall silent as Diabaté begins opening up its dynamics as if it were one of those trick cabinets filled with hidden drawers. It's an intense listening experience; a music of beauty that demands your full attention, and whose abstractions seem to flow just beyond your grasp.

Among those in the audience is his fellow countryman Bassekou Kouyaté and his band, who delivered a stunning performance earlier in the week at the Barbican. The two exchange repartee, and it's Diabaté who explains near the end that "we are at war because he did not bring his ngoni", and Kouyaté half-rises in sheepish apology.

The two together would have been extraordinary, but he's not the only great musician in the aisles, and for the encore, the Buena Vista bassist Cachaito is invited on stage to accompany Diabaté on "Ai Ga Bani", from In the Heart of the Moon.

Kouyaté's wife, Amy Sacko, steps up to sing, and Ngoni Ba lead a hand-clap support that ends with a standing ovation, bringing to a close a stunning performance.

Diabaté is back here in September with the LSO, opening a dialogue between African and Western classical music. If you're around then, Kouyaté, don't forget the ngoni.

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