It's an example of Derren Brown's brilliant use of misdirection. Here you're misdirected as to the whole nature of the trick, and if you start your analysis by asking yourself, "how does he manage to read the woman's mind?" then you've already swallowed the false assumption. You have to take a step back and start from the question, "how does he manage to convince me, the viewer, that he read the woman's mind?"
I just want to burn him at a stake and watch his witch's heart bubble. It’s extraordinary. Great trick. - Stephen Fry
Derren Brown does many amazing tricks - I want to focus here on his "mind reading". This is way beyond any cold reading I've seen, but he insists that he uses no actors or stooges. He's also a skeptic, very clear about not being psychic. He does reveal some of his tricks, but maintains a lot of mystery.
Reading David Frost's mind - unusually, he struggles and gets the first one wrong, and seems to reveal tiny glimpses of his technique. Then at the end he gives more hints about his technique than usual.
Pet name - getting someone on the street to read another person's mind. In the full version (from the DVD of Trick of the Mind, series one) the segment starts with Derren telling the guy (the pet owner) that sorry, it won't work on you, then later changing his mind and bringing him in.
Creepy clown - the detail here is extraordinary.
Watch the videos then scroll down, if you want to watch it without being influenced by me... I have a few thoughts, but they don't go very far in explaining it...
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Whatever he's doing, he's extraordinarily good at it. Some speculations: