I am sharing a very 21st-century moment with a very 21st-century opera singer. I have met Renée Fleming at the end of her much-praised run as Violetta in Verdi’s La traviata at the Royal Opera House officially to talk about her London concert next month. Unfortunately neither of us can remember exactly what she’s singing.

No matter: soon we have both whipped out our BlackBerrys and are scrolling through calendars and e-mails in pursuit of information we both ought to know. Fleming gets there first: if it’s November, it must be verismo arias (Puccini and his lesser-known contemporaries) at the Festival Hall. “All this technology . . .” she says, “it’s wonderful, it’s made us all more productive — but at least in my case it’s also tripled my workload.”

In which case Fleming, currently America’s most-loved and most-lauded opera singer, must be a pretty busy woman. Last autumn the soprano was opening the season at the Metropolitan Opera in New York with an all-Fleming gala (“the first time in history a woman had done that,” she reminds me, in her gentle and diplomatic way) in which she was dressed by John Galliano, Christian Lacroix and Karl Lagerfeld. In January she was singing, quite exquisitely, You’ll Never Walk Alone at President Obama’s inaugural knees-up. There has been a new album (the verismo disc that prompts the London concert), a premiere by the French composer Henri Dutilleux, the London Traviata and the opening of the New York Philharmonic’s new season. “Career-wise,” she says, “I couldn’t be happier right now, and I’m thinking, well, just enjoy it — for as long as I can.”

If the 50-year-old Fleming is sitting contentedly at the top of her profession, the revealing part of an hour spent in her company is how willing she is to dissect that success — and even to disbelieve it. Yes, there are the delightfully silly accoutrements of American fame that have so far included a Renée Fleming dessert (“La Diva Renée”), a Renée Fleming perfume (“La Voce”) and — she adds these to my list — both the Renée Fleming iris (2001) and its official porcelain replica (2007). Understand this level of devotion and you realise why the New York-based singer spends so much more time on this side of the Atlantic.

But what, aside from that sumptuous voice, do Americans really love about Fleming? She is, she gladly admits, a poster girl for the friendly face of her art form, a role that she has recently underlined by taking on presenting duties for the live cinema relays of Met performances (when she isn’t starring in them). “Terrifying,” she says, “but what I have learnt from it is that when I then go and sing in other places people say, ‘Oh, we really loved you introducing such and such an opera, but we thought your hair looked better the week before’ and they were talking to me in a much more familiar way. And that’s really changed, because what the public enjoy now is someone who is approachable, user-friendly, whereas what we have historically loved is the diva persona.”

That d-word used to bother Fleming, who grew up in Rochester, New York, with two music teachers for parents, ensuring that music was not some sacred mystery, but “part of my everyday existence”. At school she did make prom queen — “by default,” she snorts, “because I was the roving person, the least cliquey, and everyone knew me from singing Eliza Doolittle”. But opera was a different beast. “I worried that I was too down too earth, too accessible, too much the girl next door.”

Earth mother is a job description Fleming fits much better than diva, a feeling reinforced in person by her chunky gold bangles and glamorous art-teacher get-up. In 2004 she wrote her first book, The Inner Voice: The Making of a Singer, less a memoir than a practical manual. “It’s been helpful for young singers,” she says, “and even to their families, who’ve said, ‘Thank you for explaining to us why this is taking so long!’”

Underlying that explanation is a frank and personal narrative. Critics delight in praising the silk and cream of the Fleming soprano, which seems to alight on any music it finds with almost indecent ease. “That’s the end result,” retorts Fleming, “that it appears to be facile. And to some degree it is now, because I did all that work.

“That’s what I try to tell young singers. They’re in such a hurry to get to the art, and what I say is that you’re thinking this backwards — you have to really master the technique in order to get there.”

Now she is thankful that she had that time to improve without the glare of the spotlight. “People are jumping on very young talent and throwing them in the deep end, and suddenly they have world-class careers with enormous pressure, and very little time to actually work, fine tune or prepare. It’s too much.”

Fleming knows the cost of over-commitment. After studies at the Juilliard and a slow but steady rise, by the late 1990s her star had finally gone supernova. Then, in 1998, came a sudden series of setbacks, when in the space of a few months her marriage to the actor Rick Ross — with whom she has two teenage daughters — broke up, she was roundly booed at La Scala, Milan, and she cancelled her first attempt at Violetta, one of four new roles that she was trying to juggle. The resulting crisis — rarely discussed — was deep: at the height of her crippling attacks of stage fright, her vocal coach had to physically push her on to the stage of the Met’s new production of The Marriage of Figaro, in which she was singing with Bryn Terfel and Cecilia Bartoli.

Did she ever think of stopping altogether? “Absolutely. I came that close. We’re not talking about the jitters, we’re talking about deep, deep panic, and that every fibre of your being is saying, ‘I cannot be on that stage.’”

Therapy gave her a label for what she was suffering. “It’s called success conflict,” Fleming says, “and the funny thing is you don’t have to be successful in anyone else’s eyes. It’s how you feel where you are.” Did part of her, then, somehow want to torpedo it all on purpose? “If you have low selfesteem, and if you really make it, then it can be very hard to feel a sense of entitlement,” she says. “And when that happens, there’s inevitably self-sabotage.”

All of which goes somewhere to explain not just why The Inner Voice became an outer warning, but also why Fleming is never going to take anything for granted. The future, she says, is a mixture of consolidation, as well as two big new roles, Wagner’s Elsa in Lohengrin and the title role in Strauss’s Ariadne auf Naxos as well as more of a place for contemporary music. It’s also about somehow making sure she has time for her daughters.

And it’s about a lot more slog. “It’s never good enough,” she says, “but then I think that’s true of every performer who is self-searching. But I still really love what I do — there’s no part of me that gets out there and thinks, ho-hum, another Violetta. Other singers say, ‘Oh, I have a voice, I was born to sing.’ I would say, ‘Well, I have a voice, me and another 100,000 people. But I was lucky enough to have the personal qualities and the instinct to pursue it.’” America’s favourite diva preaches a very American gospel: no wonder they all want a spray of eau de Renée.

Renée Fleming, Festival Hall, London SE1 (0871 6632500), Nov 3. Verismo is out now on Decca

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