Archie Shepp, Queen Elizabeth Hall, London

Archie Shepp's reputation precedes him. The 68-year-old saxophonist with the trademark brimmed hat and villainously lazy eyelids who led his quartet on stage at the South Bank last week was once one of the leaders of the 1960s avant garde, known for combining free, almost boundary-less music, with a vivid anger about the injustice visited on American blacks.

So free was his playing and so radical his message that Philip Larkin, never likely to have been one of Shepp's most ardent fans, characterised his style as: "these death-to-all-white-men wails, this portentous gibberish recited in the accents of Sir Henry Irving ... this semi-farcical resurrection of the Webster breathing-down-your-neck manner. What would happen to the New Wave," asked Larkin, "if its bassists and drummers played as horribly as its horn men?"

Shepp has mellowed somewhat since then. His playing on tenor sax still contains all the screeches and top-register yelps that Larkin so disliked, but they are interspersed with formidable, slithery runs, and full-bodied, vibrato-laden long notes. As for the Webster-like breathiness, well, on Monk's "Ruby, My Dear" (accompanying a guest, the French singer Mina Agossi), several times Shepp simply blew into his soprano sax with no desire to produce anything other than that soft resonance that surrounds a note, without the note itself ever being heard. Just the hint was both effective and affecting.

Shepp's playing still stands outside the norm, although, to modern ears, less so than, say, Monk's does compared to other pianists. But, accompanied by a trio of old associates who could give a masterclass in the role of the jazz rhythm section, the result was a marvel.

Both pianist Tom McClung and drummer Steve McCraven produced at least one dazzling solo apiece. Halfway through the set McCraven stepped forward to "drum" a whole number on his body, simultaneously singing "Mockingbird" as a duet with Shepp. On Shepp's own "Ujaama", McClung demonstrated that absolute mastery and conviction at the keyboard that American pianists seem to imbibe with their corn flakes.

But as a trio they were even better - unimpeachable - rising as one to do the dynamics justice at Shepp's command. Although McCoy Tyner himself was also appearing at the London Jazz Festival, anyone wishing to gain an idea of the excitement generated by Tyner and the rest of Coltrane's rhythm section in their 1960s heyday should listen to Shepp's current band.

Imitation may be the sincerest form of flattery, and he has been much imitated, but Tyner now seems as polished and shiny as his slicked-back pony-tailed hair. Shepp and his crew, however, generated an authentic edge-of-the-seat thrill with progressions that seemed fresh, even though stylistically they are nearly 40 years old.

This was only one part of their palette of decades. The quartet could slip from era to era while still sounding distinctively themselves, from a "Round Midnight" both howling and tender to the wailing storm of Shepp's own "Hope 2". Thus the band's second number was "Ain't Misbehavin'", a Fats Waller number rarely given an outing by any modern group, to whose title Shepp's sleazy rendition gave the lie. Shepp played the tune like a man returning to his wife at seven in the morning, lipstick on his shirt, who slurs his disclaimer while a half of whisky sticks out of his jacket pocket.

Shepp's remarkable vocals - part holler, part Billy Eckstine crooning, part wicked, cackling scream - featured here, as they did on a fast shuffle blues encore and on a 1960s number about black oppression and the need for revolution. Some of these themes may seem a little historical, but dated they were not. If anyone wants to know what jazz was and what its spirit continues to be, they could do no better than to hear Archie Shepp. I doubt that there will be a more powerful and truthful expression of that spirit in the whole festival.

The London Jazz Festival ends tonight: Uri Caine, John Surman and the BBC Concert Orchestra, Queen Elizabeth Hall, London, SE1 (0870 264 9988); Future Sounds of Jazz, Barbican, EC2 (0207 638 8891)