A touch of theatre from Diana Krall

"I didn't feel like I needed anybody's permission or a time-frame," says Diana Krall. "I mean, look at those Vogue shots of Yoko Ono in hot pants recently." The 47-year-old singer and pianist is discussing the rather racy cover shot for her new album, Glad Rag Doll. Something of a homage to Alfred Cheney Johnston's photographs of the Ziegfeld girls, it finds Krall - Mrs Elvis Costello - and mum to their five-year-old twin boys Dexter and Frank looking fabulous in a basque, stockings and suspenders.

"There's a bit of a Bonnie & Clyde thing going on too," she explains. "We got Colleen Atwood [costumer for the film Chicago] to do the styling. I think a lot of people's perception of the 1920s is a flapper dress and a ukulele, but some of those Ziegfeld girls died young and tragically."

Krall and I have met in a shabby-chic hotel on Manhattan's Lower East Side. New York is home for her and Costello these days. The Nanaimo, British Columbia-born singer seems tired today and her speech is a little hesitant, but then she's been up since 6.30am, taking the twins to school. "A little more concealer under the eyes and away we go," she jokes, shrugging the shoulders of her blue pinstripe jacket.

With Marc Ribot - celebrated purveyor of grit to Tom Waits - on guitar, Glad Rag Doll is a clear departure for Krall. Hitherto a mostly smooth-operating jazz singer who has sold 15 million albums and duetted with Tony Bennett, she has now pitched her tent on Tin Pan Alley to cover a number of songs from the 1920s and 1930s. In truth, this material is perhaps closer to Krall's heart than the later-period Great American Songbook fare with which she made her name.

"I knew songs from the early 1900s long before I knew jazz standards," she explains. "My grandfather was a coal miner. They didn't have money, but they had a piano. Sunday roasts were always a time when my uncle would play and we'd go through stacks of old sheet music and sing. That's how I got to know Jean Goldkette's work with Bix Beiderbecke and Gene Austin stuff like When My Sugar Walks Down the Street.

"The Vaudeville aspect of this album is important to me too, because my aunt Jean - I take my middle name from her - moved from Vancouver to New York to work in Vaudeville in the 1920s. As a kid, I always thought it incredibly glamorous that she would do that."

Krall's labour of love was overseen by T-Bone Burnett, the veteran producer and musician whose countless career coups include scoring the Coen Brothers' O Brother, Where Art Thou?, and producing Robert Plant and Alison Krauss's 2007 Grammy-grabber, Raising Sand. Chatting to him on the phone a few days later, I suggest that, with Krall's husband being a close friend of his, things might have been a little awkward if the Glad Rag Doll sessions hadn't soared.

"You know, I didn't give that a thought," he laughs. "I'm 64 and I've been working hard for a long time. These days I only want to work with people I love and I love Elvis and I love Diana. It was great to hear her explore that Muddy Waters kind of pocket on I'm a Little Mixed Up. To me, it felt like I was working with Ray Charles or Aretha Franklin. Somebody who can sit down at the piano and lay down the law."

While the robust piano-playing Burnett alludes to is a forte of Krall's, another recent engagement required a more delicate approach. Last month, she played Fly Me to the Moon at the memorial service for Neil Armstrong. Krall was invited to do so by the astronaut's family.

"It was pretty intense and emotional", she says. "It's on YouTube but I can't watch it. I sat next to John Glenn and his wife. Those guys were the original space cowboys, out there using less technology than there is in my cell phone. How courageous is that?

"I'd met Neil when I was invited to play Nasa's 40th-anniversary celebrations for the Apollo missions. We had a glass of wine and a chat, and that was a big deal for me, because I was a total space nut as a kid and I used to build my own rockets from kits. There's a photograph out there of me showing Neil this Canadian Haida tattoo that I have. He probably thought I was a total geek."

Krall says her boys aren't really showbiz children. At the mention of them, she shows me a little Ninja figure made from Lego that was a gift from them. But it's not every child who gets to hang out with Paul McCartney, as young Dexter did.

"There was one song of Paul's he was obsessed with," smiles Krall. " He even wrote a letter to the person in the song. Then when Paul and I made this Christmas record together, Dexter got to meet him. It was beautiful to see this child who knew nothing of The Beatles' significance cuddling in Paul's lap while he explained to him what his favourite song was about."

I ask Krall about another starry studio encounter; when she produced Barbra Streisand's 2009 album, Love Is the Answer.

"It was an experience of a lifetime," she says. "When she sings, it's so special and familiar that you almost fall over."

Who: Diana Krall
What: New album Glad Rag Doll
When: Out now

- TimeOut / The Independent