The child's father is her fiancé, fellow Brit Harry Holm.
"It is wonderful news, they are both very excited and looking forward to having their new baby," Morton's publicist, Karon Maskill, tells PEOPLE.
Morton, 30, a double Oscar nominee for 1999's Sweet & Lowdown and 2002's In America, has a 7-year-old daughter, Esme, from a previous relationship with British actor Charlie Creed-Miles.
Morton met Holm, 26, in 2005, when he directed her in a video for the band The Victims. He proposed to Morton in Paris in May 2006 – on her 29th birthday.
The couple just returned to London from New York, where Morton was filming the Charlie Kaufman film Synecdoche with Philip Seymour Hoffman.
"She's been so busy, doing films back-to-back, they just have not had the opportunity to have the wedding," says Maskill.
The best man was due to be Johnny Borrell, singer with the band Razorlight (and Kirsten Dunst's boyfriend). And it looks like a wedding invite will still show up for Borrell and Dunst: He's still expected to serve as best man when the pair do exchange vows.