The Oscar-winning actress, who was bundled up in a long black coat and carrying a Prada purse, brought Joe a carton drink called Ice Box.
Meanwhile, it appears that the new James Bond movie will be a family affair for Kate and ex-husband Sam Mendes.
The acclaimed film-maker is expected to direct Daniel Craig in the latest 007 adventure some time towards the end of next year, with the production likely to be based, as usual, at Pinewood film studios.
Kate revealed that their 7-year-old son Joe and Kate’s 10-year-old daughter Mia will move to the UK with her for the period of filming.
“Sam is doing the next Bond film, all being well, and we’ll all be in England if that happens,” she says. “It’s such a massive commitment for him and it’s not fair for him to commute backwards and forwards to New York from London. It would be impossible. The children will be there with me.”
As for the current status of her relationship with her former flame? “‘We’re really good friends and have very good respect for each other,” says Kate. “I can see it, but you’d have to ask Sam what he thinks.”