The queen of Broadway in the home of jazz? It might not seem the obvious combination, yet this show, part of Ronnie Scott’s 50th anniversary celebrations, provided another excuse to wallow in the miracle that is Barbara Cook.

When she celebrated her 80th birthday at the Coliseum two years ago, some of us wondered if we would have a chance to hear her in London again. Happily, the diva shows no sign of quitting just yet. Her voice has, inevitably, lost a little of its subtlety; the timbre is huskier, and she occasionally projected too forcefully in this intimate venue. But those are mere quibbles. Unlike Andy Williams, another octogenarian who passed through town recently, Cook is still close to the top of her game. Besides, the charisma and the folksy humour are totally intact.

While she may be the toast of New York, she still has something of the wide-eyed innocence of the small-town girl from Georgia. She can be sassy too, confessing to earthy thoughts about baseball players and an opera singer, while casting a less than motherly eye in the direction of Barack Obama.

Backed by a nimble quartet, she unfurled a programme that combined urbane lyrics with bluesy passion and droll wordplay. Just to prove that she can swing as convincingly as any jazz singer, she scampered through Ray Charles’s Hallelujah, I Love Her So and pushed the tempo hard on the quaint Gershwin melody Nashville Nightingale. Confessing that she avoids Cole Porter songs, she then showed us what we had been missing as she brought barely contained yearning to I’ve Got You Under My Skin, the arrangement opening with all the quiet formality of a piano étude.

Send in the Clowns was similarly intense. An overfamiliar song, yes, but in the hands of a great singer it still sends a chill around the room. Here’s to Life isn’t in the same league at all, but just about every singer of a certain age wants to try it. Cook came as close as anyone to making the lyrics dance. Besides, her stark version of Lost in the Stars was as haunting as anything you will hear this year.

Towards the end of a magical show, the sound of a very ordinary rock band began to grind its way through from next door. It might have been a glimpse of the future. What will we do when Barbara Cook has gone?

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