STELLA MCCARTNEY is sitting in a Notting Hill hotel pouring tea from a silver teapot into a porcelain cup. Behind sits a family decked out in all-white Gatsby-esque tennis attire for dinner. “I like this tennis family, by the way,” she says. “It’s all about tennis this season. Such a look. Sweater on the shoulder—very Bill Murray, Chevy Chase. You might see that in my next collection.”

It is early on a muggy July evening, and the sun is still out. We are near McCartney’s London design studio, but she didn’t come from the office....