It’s charming to meet a star who’s starstruck. She may have sold 14 million albums but an intimate evening to honour Stevie Wonder at the White House hosted by the First Couple was almost too much for Diana Krall. “I was an emotional wreck,” the world’s premier jazz singer says. “It gives me goosebumps even thinking about it.” Krall and a select few, including Paul Simon, had been invited to perform Wonder songs. “I sang Blame it on the Sun and I was so nervous. I had my eyes shut the whole time. I didn’t sing well but it didn’t matter because it was such a love-in.”

And how were Barack and Michelle? “The two of them are tall, strong, together — a couple who love each other. And we started talking. And I say: ‘Elvis and I . . .’ and Barack says: ‘Elvis, he died’. ‘No, I mean Elvis Costello, my husband.’ And he says: ‘Really? You’ve been keeping this under wraps.’ It was so funny . . . He had no idea we were married.”

Krall tosses back her hair and laughs, but her story is not finished. “So that evening, all in my sparkly shoes, I go down to this little club with my manager. It was like a Bette Davis film in this place and the piano player was right next to the table. I started singing because I was in such a good mood [it’s something she’s prone to do in clubs] and the pianist didn’t know who I was. Then I started to play some stride piano and he said: ‘You need to work on your left hand — and your pedalling.’

“Anyway, finally he is at the table having a drink, and he says: ‘If you stick with this you might really make it.’ And my manager says: ‘She’s Diana Krall.’ And this guy goes: ‘You’re too young to be Diana Krall.’ ”

She is laughing hard now. “I’d just been to meet the President of the United States and here was a guy saying to me: ‘You think that you’re great but you’re not’.”

But the pianist was right about the age thing, the woman sitting next to me does look younger than Diana Krall. In fact she looks more glamorous than any 44-year-old jetlagged mother of twins has a right to at 9.15am. Especially one in the middle of an if-it’s-Monday-it’s-London promotional tour for her new album. She’s a svelte 5ft 8in with dark blonde hair, all got up in little black dress and heels for breakfast telly. Very different from last time I met her in 2006, when she was tired, slumped on a Claridge’s sofa, her luggage lost en route from Paris and fending off morning sick-ness. Krall, a singularly focused performer, was still touring when she was seven months pregnant.

Now, she says, she is on top of the world. So where are the twins, Dexter and Frank? “They’re back at home in New York.” Costello is happy, at the age of 54, doing the dad stuff. “He’s amazing; he cooks and he sends me videos throughout the day — at the park, meal times, bath times, singing times.” (Dad’s Pump it Up is a favourite.) Their mother will have two days back at home — “mostly sleeping” — and then she will be off travelling America in a tour bus kitted out for the kids to accompany her. Costello, meanwhile, must scoot off to promote his own album. Welcome to the lifestyle of the modern showbiz power couple.

The boys have toured with Krall since they were six months old and she has recruited a nanny from the Dixie Chicks.“It works, it’s really intense but I like it. If there’s a pool at the hotel, that helps; if there’s a museum with a dinosaur exhibit, that helps. But I’m a much happier person for having this life. My work-life balance has changed for the good."

She misses her husband, “but this is the life we chose, the life of the touring musician, and right now we’re going to go for it”.

She has just tried her hand at producing, making an album of standards with Barbra Streisand. The lyricist Paul Williams famously described working with Streisand as “like having a picnic at the end of an airport runway”. Krall says the experience was challenging but Streisand “sings her butt off”. She has also filmed a cameo, glammed up as a 1930s chanteuse singing Bye Bye Blackbird, in Johnny Depp’s new gangster movie, Public Enemies. There’s been another invitation to the White House for a Democratic fundraiser, and she has been asked to sing Fly Me to the Moon to John Glenn and other Nasa astronauts. As a girl she longed to be an astronaut.

But the biggest deal, of course, and the reason she’s whistlestopping through London, is her new album Quiet Nights. The record, her first since becoming a mother, is a set of ballads and bossa novas dedicated to Costello. The mood of dreamy sensuality recalls her world-conquering Look of Love album and Krall is clearly a little peeved at writers (including me) who found it all a little too soft-edged. “Yeah, there’s elevator bossa nova — but what we’re playing is much more intricate. People need to listen, use their ears. This is an album that comes out of a deep love of Sergio Mendes and João Gilberto.” She frowns. “It doesn’t bother me until I’m on some chat show and people say: ‘It’s just easy listening.’ And I go: ‘I suppose so. Yeah, whatever.’ In the past I would have got mad about it.”

But this, it seems, is a small cloud in Krall’s sunny outlook. The girl who grew up in Nanaimo, British Columbia, was discovered by Ray Brown, Oscar Peterson’s bassist, and spent 20 years climbing to the top of her profession, assures me that life is how it should be. She smiles as she gets up to leave — next stop Barcelona. “I just think my life is so charmed. I used to think that I wouldn’t talk about it, that I was bragging, but why not? It’s such a trip.”

Quiet Nights is out on Verve. A Diana Krall concert special will be broadcast by Radio 2 on Monday (10.30pm)

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