Fans will probably remember that Garner also starred opposite Andrews in the big-screen movies Victor/Victoria (1982) and The Americanization of Emily (1964).
"He's just adorable," says Andrews. "We're friendsÂ…from way back. And he's just such an easy man to work with. We know each other very well. It became a labor of love and pleasure."
She doesn't try to analyze the chemistry she and Garner generate on-screen. "I guess he loves to play that wonderful sort of lovable old curmudgeon, and I guess my primness comes out with that, and they pit it against each other."
One Special Night is about two strangers thrown together in a rural cabin during a blizzard, which naturally brings to mind the Hollywood classic It Happened One Night (1934), starring Clark Gable and Claudette Colbert.
American audiences haven't seen much of Andrews lately, a situation she attributes to her caring for family and the Broadway run of Victor/Victoria.
She also had surgery to remove some noncancerous throat nodules, a procedure that affected her singing voice.
"I'm optimistic and hope I will [sing again]," she says. "There are good days and bad days, and I need to work on it really hard in order to get back up again, and then I don't know what I'll discover. But right now, I'm optimistic."
Andrews also is the author of three children's books, which she writes under the name Julie Andrews Edwards. The first book she wrote, Mandy, was prompted by her eldest stepdaughter.
Andrews and her husband, director Blake Edwards, were trying to make a movie, and their household was "mayhem," she recalls.
"So, finally, in real Mary Poppins fashion, I said, 'OK, everybody, we're going to brush teeth and pick up laundry and clean up and if you don't do it, you have to pay a forfeit,'" she recalls.
"So my eldest stepdaughter, who was trying to get to know me, said, 'OK, but you play, too.' I said, 'What do I have to do?' She said, 'You have to stop swearing so much,'" Andrews says.
"I hadn't noticed I had been cussing quite considerably, and I said, 'OK,' and of course, I was the first one to lose the bet," she adds.
Mary Poppins swears???
"Gorgeous four-letter Anglo Saxon words, believe me," Andrews says.
When she asked what he had to do to make up for the bad language, her stepdaughter told her to write her a story.
Andrews also is in the process of writing her autobiography.
"I find it quite fascinating, because if you really start focusing on it, really focusing, memories come back that you really had forgotten, and things come back," she says.
"And I'm at that stage where I'm just correlating and filing and making endless notes. I'm only going to take it through my early years up to about when I came to America, to [do] My Fair LadyÂ…because I think mostly people know the rest, and it's so daunting to do the whole damn thing," Andrews says.
Is this going to be like Winston Churchill's biography? Will there be six volumes of Julie Andrews?
"I'm not that old," she says.