He hardly stopped smiling all night. But Tony Bennett has plenty to feel happy about. The singer's singer is enjoying an Indian summer that is bringing him bigger audiences and more record sales than he's had for 30 years, and almost everyone in the Royal Festival Hall seemed to feel that it couldn't happen to a nicer guy.

The great, boisterous tenor of yore has grown gravelly around the edges, and he sometimes has to shout at a note or wallop over a line that he might have breezed through once. Otherwise, though, the voice is in amazingly good shape for a man who'll turn 70 next year.

Bennett talks his way through a few songs where the melodies are so familiar that he might be chatting among old friends, yet when he came to I Left My Heart in San Francisco he still treated it with the care and respect that he first brought to what is really a rather lightweight little tune.

The feel he projects is something between avuncular and happy-go-lucky. Where Sinatra delivered real gravitas, the master mulling over the American songbook, Tony almost chuckles his way through it, enormously delighted at every line. Where Sinatra's America is a metropolis, Bennett's is a friendly neighbourhood. He opened his hands and beamed at the end of every song, as if inviting us to share in the pleasure of the whole thing. He still works with a trio led by pianist Ralph Sharon, a saloon singer's group, and this toehold on jazz is what keeps him cool: along with Gershwin and Porter, he fills his set with Duke Ellington. The only remotely modern song was Michel Legrand's lovely Watch What Happens, yet there was nothing that seemed old-fashioned.

Perhaps this heartiness prevents him from touching a deeper nerve. There were few songs of remorse or heartbreak in the set, and when he sang Autumn Leaves, the most sublime of sad reminiscences, he didn't really find the tears in it. But when he came to Who Can I Turn To, he dramatised a setpiece of astonishing power. Sharon's trio sometimes got in the way, and the pianist isn't as witty as George Shearing, let alone Tommy Flanagan. But they did the job.

Bennett has a favourite encore of asking for the microphone to be switched off and singing a couple of tunes alone with Sharon, including a windswept Fly Me to the Moon. Alone and unadorned, the great voice sounded more winsome than ever. No wonder his admirers rushed the stage at the end.