Yet she is not without controversy. At the Royal Festival Hall on Monday, she opened by stepping into the chattering cauldron of Miles Davis's electric music, adding her own lyrics to "Running the Voodoo Down" and on occasion doing her best to make her art an acquired taste. Never one to make it easy for her audiences, either singing from within the prickly thickets of her own music or using songs dug up from heaven knows where, she succeeded in making her material a personal expression of self, claiming it as her own.
Her highly personal choice of repertoire underlines the fact that back in the 1980s, she could have had the jazz world at her feet singing the well-known Broadway standards that Fitzgerald and Vaughan used to inhabit. But she never showed any interest in taking the obvious route to success, saying: "We have to take what we can and learn from the masters, but, by repeating what they do, we're not really doing justice to the tradition. I think the whole point in jazz is to establish some kind of identity and help propel the music forward, make it speak of our needs today."
Her accompaniment, a piano, bass and drums augmented by two guitars and a percussionist, is intended to distance herself from Holiday, Fitzgerald and Carter. When in 1993 she signed with Blue Note records her artistic vision came into sharp focus under the direction of the producer Craig Street.
Three exemplary albums with minimalistic backings followed, exploring the expressive and emotional force of her voice, which delivered on the enormous promise she had revealed since making her New York debut in 1982.
Her current album, Travelling Miles, provided a subtext to her concert, drawing together several compositions with a Davis connection, including her own dedicated originals. Stripping songs down to bare skeletons and sometimes accompanied by just an acoustic guitar and percussion, the dark timbre of her voice gave vivid personal meaning to lyrics, a gift that can be scary, as Billie Holiday showed. Now she's getting closer to the singer she always wanted to be: a singer of the past, the present and the future.