Of all the UK's 1960s pop survivors, Georgie Fame must be the coolest, and when you see him in a small club, behind an electric organ, leading his band and singing vintage material with a mellow voice, you realise why. He never pushes it too hard; he doesn't have to prove anything. That's true of the Blue Flames, too. On Anthem for a Band, the front line of Guy Barker (trumpet) and Alan Skidmore (tenor saxophone) produces a thick warm timbre - the thrilling sound of world-class jazz soloists keeping it simple.

Fame loves his jazz, but he's a pop artist, too. He has steered his repertoire into a sector of hip 1960s culture that's neither faded counter-culture nor bland cabaret. A "name-dropping monologue" (dedicated to Stanley Holloway) name-checks Cassius Clay, Henry Cooper, Dexter Gordon, Sonny Stitt, Christine Keeler, Lucky Gordon, Percy Mayfield, Joe Williams and many others over a slow groove.

When they play Jenine, with its Eddie Jefferson lyrics, Fame recalls the excitement of first hearing the Cannonball Adderley album the tune came from - "If you know the record, you'll know they did a natural fade: nobody twiddled no knobs!" - and the band follow suit with a beautifully executed acoustic fade.

Fame's rhythm team - sons Tristan and James Powell (on guitar and drums) and bassist Alec Dankworth - define a particular kind of deep swing. They play the bebop of Symphony Sid with an unhurried pulse that takes the music back to its Kansas City roots. Barker delivers a great trumpet solo that prompts Fame to join in with more vocalisation. He encores with a "last waltz", Mose Allison's touching song Was, which sends us home happy to have been in the presence of genuine cool.

· At the Jazz Cafe, London NW1, on January 28. Box office: 020-7344 0044.