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Big-name stars showed up to the Roundhouse club in Camden, London, on Sept. 24 to catch a concert by folk-rock band Mumford & Sons: Gwyneth Paltrow, Chris Martin, Carey Mulligan (who is married to the band's frontman, Marcus Mumford). But no one caught the attention of the crowd-or the band-quite like Adele. The very pregnant pop star was in the crowd with her boyfriend Simon Konecki and, according to an audience member, was "happily singing along." Even Mumford himself couldn't ignore her presence. "Marcus name-checked her from the stage," says the audience member, "and she gave a little wave."

That date night with her boyfriend was a rare public appearance for the very private superstar, who all but vanished from the spotlight after winning six Grammys in February (plus two BRIT Awards nine days later) for her massive second album, 21. Long before she became one of music's biggest stars, she told PEOPLE, "I don't think I always want to be the one in the front limelight." So unlike most of her peers, Adele, 24, hasn't toured (she canceled her U.S. and British dates back in 2011 because of a vocal hemorrhage), refuses most interview requests and has made no red-carpet appearances since February (though she quietly attended two awards ceremonies in the spring). And even though she's topping the charts once again with her hot new James Bond theme "Skyfall," she has no plans to change her course. "Adele has no interest in any of the parties and premieres she gets invited to," says a source who knows the singer. "It's just not her thing."

Her "thing" these days? Getting ready for the birth of her first child, which a family source says is due this month. "She is just thrilled," the Adele source says of the singer, who surprised the world when she announced the big news on her website in June. Just two years ago the sassy Brit was still getting over the breakup that inspired her hits "Someone Like You" and "Rolling in the Deep" and often spent evenings in a pub with her pals. But all that changed when she found love with Konecki, 38, who was first spotted with her this past winter; she soon became pregnant. "I really want to be a mum," she told PEOPLE in 2008, adding that she hoped to have three sons by the time she's 30. "I better start getting on with it!" And now that she is well on her way, "she is like a different person," says the source. "She's given up smoking, and she hasn't had a drink in months. Life is pretty much perfect for her right now." Lady Marina Cowdray, a Konecki pal, agrees: "They're super-happy."

As Adele's due date nears, she and Konecki (who has a daughter with his ex-wife) have been staying in West London, where she's been spotted walking her beloved dachshund Louie in nearby Hyde Park. Preferring dinner parties at home to going out to clubs, "she is totally laying low and nesting," says the source. "She's enjoyed picking out furniture for the baby's rooms and trying to choose names."

The mom-to-be also squeezed in time to work on "Skyfall," which she only recorded about six weeks ago, says the film's producer Barbara Broccoli: "She spent a lot of time working on it and getting it right." (And she did: Within days of its Oct. 4 release, the single rocketed to No. 1 on iTunes Top Songs and reportedly sold at least 200,000 downloads.) Originally Adele was hesitant about signing on to the project-"She thought it would be too cheesy," says the source-but Broccoli says she took it "incredibly seriously." (She even insisted on reading the script.) "She was worth waiting for," says Broccoli, who was impressed with more than Adele's voice and songwriting skills. "She's very down-to-earth and unaffected by fame. For someone so young, she has this wonderful wisdom. And she seems to be very sure of who she is."

And that, of course, is a secret to her success. Other stars would be making every effort to stay in the spotlight and capitalize on their fame; her manager recently told Rolling Stone that with her maternity leave, no one knows when there might be another Adele album. "She is winning and leading because her plan is her own plan," explains former record exec Charlie Walk, now chairman of the brand marketing company JWalk. "Adele reports to Adele."

Soon enough, she'll have a new master-her baby-and both Adele and Konecki plan to keep their child out of the public eye. "Neither she nor Simon want to bring the baby up in London," says the source. "She says it's like a goldfish bowl." The happily unwed couple ("I'm not married ... Zzzzzzz," she tweeted after rumors surfaced in August) are renovating a four-bedroom home in the seaside resort town of Hove, close to Konecki's office, where he is head of the clean-water charity Drop4Drop. When she had lunch with friends at the local restaurant Ginger Pig on Sept. 27, an observer says the singer's presence caused little stir. "She just had a burger and chips and a glass of water," says the witness. "Everyone just left her alone to enjoy her lunch."

And the British press-who have always supported her-seem content to let her have her space. She's never been a high priority for paparazzi, and now, in the wake of the phone-hacking scandal in England, tabloids have eased up on their ruthless chronicling of celebrities' everyday lives. "Privacy law has become significantly more rigorous, and as a result of that, there is much more protection [of celebrities]," says London-based media lawyer Mark Stephens.

Surely Adele is grateful for that. Though she has been invited to the London premiere of Skyfall on Oct. 23, no one's expecting her to attend. Besides, by then, she could be busy with a newborn. "[She and Simon] want to keep a very low profile when the baby is born," says the source. "I think we'll see even less of them than ever!" Few people question her motives. "Despite her millions, she is going to give the baby the most important thing all children need: love," says the family source. "The baby is very lucky to have such a special lady as its mother."

  • Contributors:
  • With Phil Boucher/London,
  • Nadia Cohen/London,
  • Dimi Gaidatzi/London,
  • Simon Perry/London,
  • Mary Green/New York City,
  • Elizabeth McNeil/New York City.