It has been six years since the ill-advised poster campaign that posed the question “Who is Dave Matthews?”, and most people in Britain are still none the wiser. It hasn’t stopped the South African-born bandleader from Charlottesville, Virginia, from continuing to sell many millions of records in America, or from filling Wembley Arena on the only British date of his current European tour.

Matthews is the ultimate antidote to the cult of celebrity. Impervious to all known varieties of hype, he inspires adoration, loyalty and respect purely for his abilities as a singer and songwriter and for the incredibly developed musical talents of his band, which he convened in 1991. Standing at the front of the huge Wembley stage in his plain jeans and brown shoes, Matthews looked more ordinary than most of the people in the audience.

He complained of having a “scratchy” throat, but promised to “squeak my way as best I can for y’all”. Naturally, he did far more than that, singing in a gruff, soulful voice, full of hard-earned experience while playing scene-setting parts on an acoustic guitar with a discreet but distinctive touch. The five men arranged behind and around him were hardly a conventional backing band, more a gathering of virtuoso talents, all bending their skills in the service of the collective whole.

Located in the American “jam band” tradition started by the Grateful Dead, numbers such as When the World Ends and You Might Die Trying were beautiful songs that drifted by precise degrees into long instrumental odysseys. The rhythm section of the bass player Stefan Lessard and drummer Carter Beauford seemed able to underpin any sequence or time signature, however innocuous, with a patchwork of effortlessly joyful syncopations. The ambidextrous Beauford in particular was an astounding player, and this was one of the rare occasions when one felt slightly let down by the lack of a set-piece drum solo.

However, there were plenty of solos elsewhere – from the violinist Boyd Tinsley, the keyboard player Butch Taylor, the trumpeter and trombonist Rashawn Ross and the saxophonist LeRoi Moore – all overseen with a quiet authority by Matthews, who maintained an extraordinary balance between the flow of the ensemble and the free expression of the individuals.

The guitarist Tom Morello, formerly of Rage Against the Machine, joined the band for two numbers – #41 and Satellite – during which he conjured some extremely strange and colourful sounds from his guitar and pedalboard.

Drawing with equal facility on the techniques of folk, jazz and rock, the band played for well over two hours, by which time it seemed as if they had barely scratched the surface of either their repertoire or their extraordinary fund of musical talent.

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