Chick Corea might be an international jazz celebrity with four decades of fame behind him, but he arrived to his solo-piano concert at the Barbican as if mooching into his studio to practise, looking surprised to find a waiting crowd. It was as if he mischievously intended to deliver the diametric opposite of a Keith Jarrett gig. He chatted breezily to latecomers, looked perplexed about what to play next, and even invited audience members onstage to tinkle the keys with him. It could have looked contrived, but the upshot was both familiar and fresh, virtuosic, personal and unexpectedly charming.

Corea unpacked a mix of standard songs, originals, and a Stevie Wonder tune segued into a straight-played Chopin mazurka (no 13 in A min, Op17 No4). To this he added a jam with saxophonist Tim Garland, Egyptian percussionist Hossam Ramzy, and eventually the singing audience for his encore. In the first half, he played Jobim's Desafinado, Ellington's Sophisticated Lady and Bill Evans' Waltz for Debby, with their regular rhythms twisted, and their melodies often diffused in free-floating washes of sound.

But if the waltz in Evans or the Brazilian sway in Jobim came and went, Corea kept the tunes whispering seductively in the background. His reharmonising was quirky but compatible, and a version of Thelonious Monk's Work – played from a transcription – came devotedly close to the originator's gritty logic and jagged chording.

Later on came Corea's own playful dances, Spanish harmonies, rich embroidery and compelling hooks (in the sophisticated Yellow Nimbus and a selection of his bright and shapely Children's Songs). A bashful volunteer called Ian and the fine UK pianist Nikki Yeoh successfully accepted his challenge to jam a couple of duets – with exhilaratingly free-flowing results in Yeoh's case. Corea looked and sounded like a man still excelling at what he loves most, and – for all his 20 Grammies and jazz-celeb stature – he was generously happy to share the privilege.