Jimmy Scott, Ronnie Scott's, London

Because of the current media frenzy – for which Jimmy Scott has waited most of his 77 years – a few more people know his story now. They know about the joys and the far more numerous tragedies and strokes of bad luck that have fallen upon him like rain, and which he has weathered with quiet endurance. So when he comes, at 10.45pm, on to the stage, and trips and falls, and grins; then when he opens his thin mouth, in a face like a very old, very tired baby's, above an attentuated, shaking frame, and starts to sing – well, he could moo and get an ovation. Instead, as his hands sweep to indicate his body, he shrugs, smiles and coolly scats: "All of me. Why not..." – quizzical eyebrow – "take all of me?" It's about time.

Here's the story: one of 10 children, Scott was born in Cleveland, Ohio, to a single mother who died in a car crash when he was 13. He already had the family ailment, Kallmann's syndrome, which stopped his growth at boyhood and gave him his eerie voice, an imploring alto vibrato. Scott began playing clubs, gaining fans (Charlie Parker, Billie Holiday) and making enemies – one of whom surfaced when, in 1962, he recorded the unutterably tender Falling In Love Is Wonderful. It should have established him alongside Tony Bennett or Nat King Cole; but Herman Lubinsky, the head of his old label, claimed he owned Scott's contract and had the album pulled. Cue nosedive; Scott found himself hustling for work, became an elevator operator, drank, failed at four marriages. It took 30 years of obscurity before he was rediscovered, and this year Falling has at last appeared.

Now everyone wants the man, just as his voice is beginning to let him down. But what he did was hung on pain, and that quality's become so heightened that this evening he sounds like a breaking Judy Garland. It's not always a pleasant sound – sometimes it's scary, and these days he can't guarantee to hit his note – but he feels what he sings like almost no one. Midpoint in "But Beautiful", he sucks his gums, screws up his eyes, lifts a hand limp as a greyhound's paw and whispers, "If you were mine/ I'd never let you go" – and he means it. When he cries, "You don't know what love is!" he's resentful and destroyed, and the words are wretched with the empty ache of hurt.

At times such as this he's ageless. At other times, he's confused and turns repeatedly to the wrong page of his score, or stands, lost, amid the band, seeming to struggle the few feet back to the mic. Late in the set he extemporises on "Sorry Seems to Be the Hardest Word", homage to his new idol Elton John, but not the most poetic of choices. If he's falling into disarray, the band are his safety net. They make a featherbed of "Embraceable You", Marshall Keys's sax just a murmur and drum barely grazed, and turn "Pennies from Heaven" into something really special.

And then, just as you think he's being carried, Scott reaches into his soul and delivers "Sometimes I Feel Like a Motherless Child", which has all the bleak power of Holiday's "Strange Fruit". His soaring voice sounds like a boy's and, though you know that things are better now, you know how hard it's been. It's almost voyeuristic to watch it, an exquisite theatre of horror. Jimmy Scott has earned all of our regard.

To tomorrow (020-7439 0747)