Surely, Derren Brown's team talked to the lady, asked her a few questions like her name, her age, her dogs names etc, and fed that information to Derren. It's very easy with a few pieces of information like that to completely narrow it down to one person. You can see in the video, he asks for all the Fs to stand up, and he selects one person.

I'm sure there's more to mentalism, like reading body language but it feels like 90% magic (lots of prep work + hard work + presenting / misleading) and 10% improvisation.