The couple was together inside the house for two hours, then Mc Cartney drove away with Arquette hidden in the backseat, the News of the World said.
He drove down the road and pulled up alongside a taxi, which took her back to the home of friends in London.
Arquette - the thrice-divorced sister-in-law of actress Courteney Cox - has a history of dating pop singers, including Peter Gabriel.
She appeared in "Pulp Fiction" and "Desperately Seeking Susan," and won an Emmy nomination for her role in the TV film "The Executioner's Song." Mc Cartney is in the middle of a protracted and acrimonious divorce from his second wife, Heather Mills.
(Nancy was also diagnosed with breast cancer in the late '90s but was able to beat the disease.)Like Linda, Nancy comes from a wealthy, East Coast background, and the fact that she has her own money (and isn't after Paul's) supposedly "makes everyone comfortable," including Paul's daughter, Stella Mc Cartney, who is said to have been won over by Nancy's "calmness, class and slightly hippy nature.""Paul is deliriously happy with Nancy and decided she was the woman he wanted to make his third wife.
LONDON - Yet another woman wants to hold Paul Mc Cartney's hand.
Only three weeks ago, Mc Cartney, 65, was seen strolling in the Hamptons with Shevell, 48. "I'm sorry, I don't want to talk about it," she said and then turned around and went back inside.