But there was one restaurant name Kai could never forget: Nobu. "Kai really likes Japanese food," says Connelly. "It's big, and it's in the Metropolitan hotel. You walk in and there's a big bar and people hanging about. To Kai, it's a super fancy sushi restaurant, really special. He likes rolls with extra ginger. No wasabi, extra ginger."

After lunch, they were on the run again, sometimes to Hampstead Heath, where Connelly lived when she was 14.

"They have great swimming ponds," she says. "They were having an unprecedented heat wave. One hundred and eight degrees. I was trying to sneak Kai into the Women's Pond. But it didn't work. It's definitely for women only. I thought, 'Women and six-year-old boys.' But it's definitely a place to go back to, really great. There's a Women's Pond, a Men's Pond, a Mixed Pond."

Despite his mother's best efforts on his behalf, Kai was more interested in exploring than swimming. I can see him tugging at her arm and leading her back into a cab, directing the driver to take them straight to the Tower of London, the 900-year-old edifice that no six-year-old (or 60-year-old) can resist. "Kai loved it," she says. "It's not just all tower. It has a moat around it and turrets and different towers. There's the collection of crown jewels and it has armor. Then, in the fields outside, they do jousting and re-enact sword fighting."

She is re-enacting her three months in London now, reeling off place after place that she and Kai visited: the Tate Modern, which she calls "awe-inspiring"; rowing in a wooden skiff on the Thames River in Richmond in West London, where she and Kai would pass Eel Pie Island (Henry VIII used to stop there for lunch while hunting) before rowing up to a pub for a lunch of their own; Legoland, near Windsor Castle, "a big hit"; the fish market, "I did lots of cooking"; Buckingham Palace … all of the landmarks of what she calls the "heartbreakingly beautiful city." The only thing she didn't get to do that trip was to take Kai to Paris via the Chunnel. "It's just a wonderful thing to be able to do, and I kept wanting to, but didn't get around to it," she says.

Then, almost three months were gone, and her husband had a rare day off. So ­Connelly, Bettany, Kai, and some friends walked miles through Hyde Park, attending a crazy only-in-London event called Red Bull Flugtag. It was, she says, "a competition where people built these flying machines that went off this ramp, and they would see how high the machines could fly before crashing into the water.The most absurd thing. But I think we walked miles and miles in the heat, with these massive crowds. It was so crowded, you could hardly get close enough to see what was going on. I do remember we walked practically all the way across the park in this heat wave."

The next day, Connelly went into labor.

She checked into a birthing center just down the way from Abbey Road, where the Beatles had offices and a recording studio, and where they were photographed walking across the famous crosswalk for the cover of their album Abbey Road. Bettany, Connelly, and Kai found themselves crossing that famous striped crosswalk again and again. "I was in labor, sort of trying to make things go quicker, walking down Abbey Road, taking a break from the birthing center," she says, laughing at the improbability of it all. "As a huge Beatles fan, I mean, Abbey Road! Pacing, fretting, worrying. But very much entertained in the meanwhile. I'm not sure you're allowed to go into the studio, and we didn't really try. But just seeing that street sign and that sidewalk was quite cool."