On Jan. 5 actress Sienna Miller all but floated out the door other London apartment and greeted reporters by declaring: "I'm the happiest girl alive." Perfectly understandable. The press had gathered outside her Notting Hill home because, as of Christmas Day, she was engaged to marry Jude Law, 32, PEOPLE'S latest Sexiest Man and Britain's Busiest Star, with six movies released in just the past year. One of those was Alfie, the film that brought the two actors together when it shot in the fall of 2003. "I want a big church wedding," she continued, beaming almost as brightly as her big engagement rock: nine diamonds in a platinum circle set in gold. "We haven't set a date yet, but I'm ecstatic."

Law popped the question just before the couple headed off for an island vacation with Rafferty, 8, Iris, 4, and Rudy, 2, his children by his ex-wife, fashion designer Sadie Frost, 39. Although Law's publicist, Ciara Parks, would give no details about the engagement scene, she said that Miller did accept on the spot. Duh. "They are both thrilled, absolutely over the moon," says Parks. "As are their families." That includes Frost, whose 2003 divorce from the actor was an emotional low point for both of them. "I'm delighted for Jude and Sienna," Frost told People in a statement, "and wish them all the best for the future." According to one source, Frost, who's now dating twentysomething flamenco guitarist Jackson Scott, "knew it was [in] the cards."

Law and Miller were never exactly playing their hands close to the vest. When they first met for Alfie, in which he played a swingin' cad and she was one of his girlfriends, "they came and did this little screen test at my house," says director Charles Shyer. "Nothing was happening between them. It just kind of evolved over a period of time. It was real natural." And it quickly swamped both of them. By the time the cameras were rolling, when a romantic scene would end, they kept on going, says one witness from the set. There were hugs, intimate giggles, and "she would run her hand through the back of his hair." Between takes of a scene with the two of them on a scooter, "she had her legs wrapped around his waist."

The romancing continued when she went to Venice last fall to shoot a movie about Casanova with Heath Ledger. Law followed, sometimes turning up with the children and a nanny, more often by himself. "He would spend hours waiting for her to film her scene," says one insider from the set. "They would walk down the little canals with their arms around each other, stopping to kiss. They aren't that well known in Italy, so they could wander freely."

That's not the case in London, where Law's personal life has been closely watched in the few years since he became a star. The sad, slow dissolution of his six-year marriage to Frost made headlines for months; at one point she was hospitalized for postpartum depression, and on one occasion police were called after the two exchanged heated words.

Things with Miller have been outwardly less dramatic. "She's very much a free spirit," says one source who knows her from Alfie. Previously linked with model Dave Neville, she has quickly become a British style icon with her waif-chic charm. At the end of a day in period costume for the movie with Ledger, "she'd leave her whalebone 1700s silk and taffeta gowns," says a source from the set, "and slip into tight jeans, baggy boots, 1970s Ray-Ban glasses and little hats."

Don't look for that on her wedding day. "It's always been my dream," she says, "to marry in white."

Tom Gliatto. Simon Perry in London, KC Baker in NewYork City and Praxilla Trabattoni in Rome

  • Contributors:
  • Simon Perry,
  • KC Baker,
  • Praxilla Trabattoni.