ANNOUNCING DRYLY that your next number is by an ex-Governor of the state of Louisiana is hardly likely to quicken the pulse of the audience, but Mose Allison's version of Jimmy Davis's "You Are My Sunshine" turns out to be something of a showstopper.

Completely contrary to the song's traditionally jaunty appeal, Allison makes it into a slow, achingly tender, loser's lament for lost love, thwarted ambition and wasted years. And as he sings he throws his head back like a hound dog howling at the moon, his fingers pounding at the keys of the piano to draw out a painful, Southern Baptist dirge of starkly dissonant chords. It's like his fellow Mississippian Elvis Presley's early Sun Records version of "Blue Moon" before it hits the rockabilly beat, only with added irony - never Elvis's strongest suit. On his own songs he's even better, setting the blues to mordant lyrics whose satirical wit recalls the work of fellow songwriter Tom Lehrer or the cartoonist Jules Feiffer.

Allison is a performer so idiosyncratic and eccentric, he really is in a company of one. Now 72 years old, he's famous in this country - insofar as he is famous at all - as a stylistic model for the early work of Georgie Fame, who covered his tunes on his first album and has continued to echo his unique expressionist vocal style. John Mayall and Van Morrison also dipped into the Allison repertoire for songs and inspiration in the Sixties but, really, no one sounds remotely like him. Indeed, not many would want to, for his voice is more self-willed than God-given.

The Allison style is derived partly from the early piano trios of Nat "King" Cole and his imitators such as the sophisticated bluesman Charles Lloyd. But while he keeps the rolling blues metre, intimate approach and drawling vocals of his antecedents (or perhaps contemporaries, for he is barely any younger), Allison subverts them through the comedy of his lyrics. "Ever since the world ended," goes one of his blues songs, "I don't get out much any more." He also sounds more country than his black forebears, a trait commented on in the number "White Boy Stole the Blues".

Looking like a distinguished American college professor with a grey beard and a bald pate, Allison does whatever he wants to do, and the hard-pressed rhythm section of Roy Babbington on double bass and Mark Taylor on drums more or less has to wing it, looking out for boy- scout signals from Allison about changes in the tempo or duration of each song. As a pianist Allison is, rather like the early Nina Simone, a Bach- meets-the-blues devotee, with a harsh, percussive style, a predilection for long, fugue-like structures, and a blind disregard for the normally neat symmetry of the metrics of a song, which change alarmingly according to his whim. Basically, he doesn't give a toss, and he alters the pattern of a song or the presumed plan of a set-list whenever he wishes to, in impeccably improvisatory fashion.

To be sure, Allison's style is preserved in aspic from the "age of anxiety" of the 1950s and early 1960s, when Playboy was hip, shrinks were in vogue, and jokes about tight-assed, narrow-tied organisational men were relatively new. But he has managed to update his conceits very effectively, affecting a rather old-fashioned impatience with the tics of contemporary life. In the midst of a song about faxes and mobile phones as modern fetishes, a phone went off in the audience, as if to confirm his concern.

But after seeing Allison, what you take home with you, more than the sly wit of the slightly corny lyrics or the perfectly-formed drama-in- miniature of the songs, is the rattling rhythm of his piano-playing and the barked-out syllables of his voice, with the bassist and the drummer looking urgently in his direction, desperate for clues as to what will happen next. At his best, Mose Allison is still, at an age when he should be looking for his pipe and slippers, nearly dangerous.

Mose Allison: Pizza Express Jazz Club, W1 (0171 439 8722), to 1 Feb.