I studied a lot about magic routines and can tell you for many big magic tricks on youtube at least one possible way how it would work. But the most important thing about magic is, it is entertainment. And also Derren Brown is an entertainer, that's what he does. I'm a big fan of Derren, also because he exposes much of the supposedly psychic or prayer stuff.
I clearly agree with garethrees' point about misdirection and psychology. Providing a solution that seems plausible to system 1 (sensu Kahneman), makes you stop thinking about it. I think that one of Derren's best tricks is to make the audience feel happy with a fake explanation. In general, I don't like exposing magic tricks. But in some cases when false beliefs spread by magicians clearly threaten to poison people's belief systems, I make sort of an exception:
Forget suggestion and NLP in the way Derren uses them as explanations. All his tricks are clearly possible without them.
There are tricks that do work with suggestion. In general if the audience expects a card trick, do a trick that's build on suggestion. If the audience expects a trick based on mind reading do slight of hand.
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: