Competitiveness can be healthy, Sophie says, as long as you don’t lose perspective.

Every morning, Sophie Hicks walks across the roof terrace that connects her home to her architecture firm. “That’s an odd bit of routine,” she confides, dressed in a sharp collared shirt and glasses. Despite living amid the abundance of restaurants and boutiques in London’s Notting Hill neighborhood, Sophie remains steadfastly enclosed within, always eating lunch at her desk and then swimming laps in her pool once the day ends. She is, says a colleague, “working while she’s walking.”

This relentless efficiency has packed a lot into the past four decades. First, there was Sophie’s 10-year career in fashion, which included plum jobs as a fashion editor at Tatler and British Vogue in the ’80s. She also acted in a Fellini film, worked as a stylist for her friend Azzedine A...