In the midst of a great debate about the future of the U.S. news business, the British are coming.

Katty Kay, the veteran BBC newscaster, is set to launch a new deep-dive interview program that will take her away — not permanently — from her usual role covering U.S. politics in favor of long-form conversations with interesting figures. In the first nine-episode season of “Influential with Katty Kay,” the journalist will interview actor Wendell Pierce, dancer Misty Copeland and author Ken Follett, among others, all in a longform format that will put emphasis not only on what makes them famous but also some of their interests.

“You interview people in one way in news or politics. You are trying to catch them maybe saying something they don’t necesssarirly want to say or in an unguarded way. There’s a combative nature, which can be exhilarating, but it’s definitely combative,...