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Barclays Cheltenham Jazz Festival, Town Hall and other venues, Cheltenham

An annual festival rounds up some fab singing, and a great discovery

Sings like Billie Holiday, talks like Billie Piper. That's Paloma Faith, the supremely perky vocalist for the Cheltenham Jazz Festival's concert with the Guy Barker Orchestra on Bank Holiday Monday, broadcast by Radio 2 the following night.

It could have gone very badly. A relatively untried (at least for this gig) 24-year-old pop ingenue was going to be tied to the mast of a 42-piece band – the light entertainment equivalent of the Titanic? – to ride the swells of a thematic song cycle about lost love, heartache and, as Paloma put it, being dumped.

There was even a big concept title – "Down at the End of Lonely Street" – and a film noir subtext of doom, gloom and wobbly dissonance. Unusually for a radio production, there was also a set: a sofa, telephone table and standard lamp combo to which Ms Faith repaired between numbers, although she stood centre-stage for almost the entire 90 minutes of the action, carrying the show as well as fronting it.

After Guy Barker's introduction told of how he and Paloma had first met at Soho's Black Gardenia club and bonded over a shared love of old jazz and blues, the orchestra came in with some marvellous, Miklos Roscha-like opening-titles music. Sound effects of thunder and rain cued Faith's just-dumped entrance from the stalls, dressed as a vamp and crying her eyes out. Then she climbed on stage, went into "Lover Man" and we were away, in an almost unbroken sequence that lasted until "Good Morning Heartache" two dozen songs later.

Young, white Billie Holiday impersonators are hardly news, but Faith is so much more than that. Her versions of the great Etta James song "At Last" (the one Beyoncé sung at the Obamas' ball), and Dimitri Tiomkin's "Wild is the Wind" were convincingly soulful, and her sparky persona buoyed up the whole show. She did a fan dance, a burlesque shimmy or two, and, as her confidence grew after an early falling-off-her-platforms slip, made funny ad-libs.

The danger is that Faith risks becoming a PG-rated, gran-rock version of Amy Winehouse – one who actually turns up – but surely this won't be the case. If she started to use her own Stoke Newington intonation she'd knock polka-dot spots off Lily Allen. At the final reprise of "Upside Down", there was a total standing ovation.

Christine Tobin, who performed earlier on Monday, has a voice with all the lived-in qualities that Paloma Faith aspires to. It's what to do with it that's the problem. Her latest project with the excellent Liam Noble on piano is "Tapestry Unravelled", a jazz gloss on Carole King's 25 million-selling 1971 album, and it's great. Familiar songs such as "It's Too Late" and "You've Got a Friend" are taken almost straight, Tobin's brassy belter's voice emoting the lyrics without recourse to grandstanding effects. A thrilling "Will You Love Me Tomorrow" was done dead slow, Noble's spare chording revealing the bones beneath. Can we have Laura Nyro next, please?

The group Polar Bear, who played to an impressively large audience in the Festival's new Jazz Arena (it's a tent, but it works) were announced as representing everything that is best about new British jazz, but I have to disagree. The players are talented but to my ears this is pretentious, Nathan Barley faux-jazz, every musical phrase appearing in quirky inverted commas without a genuine emotion in sight. When the guitarist/knob-twiddler "Leafcutter John" blew up balloons so he could sample the air escaping from them, I wanted to "murder" him. This band have been going now for nearly a decade, so why haven't they got any better?

By contrast, the best new stuff I've heard in an age came from the Birmingham-based Irish composer Sid Peacock, whose young, 16-piece big band played inspiring, wildly creative music of avant-garde bite yet emotional weight. Premiering works written while Peacock was on a recent residency at the Irish Cultural Centre in Paris, the orchestra (two violins, marimba and congas added to reeds and minimal brass), handled the difficult idioms with great skill.

His witty titles – "Bronze Bling" (about the Olympics), "Pixel Rampage", "Hallucinogenic Garden" – are pegs on which to hang intricately tesselated, complex cycles of competing motifs, as well as melodies that are both intellectually satisfying and funkily corporeal. You could mention Steve Reich, but this is actually enjoyable. Give Peacock an award, quick. The album is out this summer.