That question is trickier to answer than it really should be. (This might get a bit long)
Derren Brown knows hypnosis for sure. That's how he actually started performing. Some stage hypnotists will say he's not doing proper hypnosis because he doesn't necessarily follow the old-school, Encyclopedia Of Stage Hypnosis style inductions and such. Even Derren has said that he's not sure how much of it is purely social compliance and how much of it is any kind of altered state of mind.
To expand on that, there's absolutely no consensus on what Hypnosis is. There has been studies done that do seem to indicate there is, in fact, a measurable alteration in brain function when in an 'hypnotic trance'. They measured the movement speed of people's eyes in and out of trance and found there was a distinct difference. To date, to my knowledge, that is the only study that has given any kind of definitive statement like that, though I also believe the study has been repeated to similar results. Not sure on that, though.
So whether or not Derren, or anyone else, is using "Real" hypnosis is nearly impossible to properly answer because no one actually knows what 'real hypnosis' is.
What I can say, having watched the vast majority of his TV specials and seen him live in NY, is that he does the same sorts of things I do when I hypnotize people - so I say he does use proper hypnosis in his shows. He just has enough of a reputation as a hypnotist and mental manipulator that he can skip over a lot of the process that smaller names would have to use to establish that reputation and rapport.