Michael Garrick, Queen Elizabeth Hall, London, ****

After Gilles Peterson's much-hailed recent compilation of near-forgotten British jazz from the Sixties and Seventies, Impressed!, it is to be hoped that Michael Garrick's name is more familiar. It certainly should be, for this sprightly elf of a man is not only one of Britain's foremost jazz educators, but has also been at the centre of the musical strand that I would argue has been this country's greatest contribution to jazz.

Perhaps Garrick's own idiosyncrasies have militated against a higher profile. His conducting of the 16-piece big band featured much bottom-wiggling and air-punching, while an explanation of the varied repertoire he performs ended up as a conversation with a heckler, ending in Garrick rushing to the piano to play an impromptu Pinetop Smith boogie-woogie to prove his appreciation of the past. To hammer it home further, his band launched into a stunning version of Benny Goodman's "Sing, Sing, Sing", with the brass section, featuring Garrick's son Gabriel and the excellent Mark Armstrong on trumpets, ripping into the repeated motifs while Alan Jackson pounded out Gene Krupa's famous tom riffs with relish.

Garrick's extraordinary range encompasses spoken poetry, slinky cabaret numbers and delicate, pretty waltzes – even at his most experimental, he is always melodic. But with his own music Garrick is also a terrific orchestrator whose loosely-tethered sections pass and bump into each other like icebergs – clenched-fist brass crashing into loping lines from the reeds, sometimes missing as the underlying currents keep them apart, allowing an amount of breathing space that other arrangers might think risky. Very tight sections give way, and then mop up, after Garrick encourages a series of players to compete in free-jazz solos. At times it's cacophonous, but it's a vital, joyous cacophony.

Some of his compositions are orchestrations of solos taken by players in prior performances; this is jazz feeding upon itself and then reproducing in the most creative way. The best are those like "Dusk Fire", which Garrick recorded with the Ian Carr-Don Rendell group in 1966. Rendell, 77 and stooped but still commanding on soprano saxophone, stepped up to perform this with the band at the end of the concert.

This is an exploration of rural England, a countryside not of daffodils and walks, but an ancient pagan land where craggy escarpments lower their brows to acknowledge a Mother Nature beyond good and evil. The querulous soprano saxophone battles on as the lines of dissonant brass march down like storm gods from the sky. Underneath it all a relentless ostinato riff on the bass and left-hand piano strike on, a never-stopping pendulum.

It is timeless. It is utterly compelling. And it is some of the most thrilling jazz you could ever be lucky enough to hear.