I've been having the same problem - at first, I'd sit up and try to revise, because that usually wears me out (!) but it's stopped working and over the past few weeks I've found myself lying awake until 3-4am. The panic at the thought of not being able to sleep and failing exams didn't help either! What I did was I set my alarm clock for later that morning, so I got maybe three hours sleep, then got up and made sure I didn't stop until 11 (this was in a non-exam week, btw!). I was able to fall asleep within 30 mins, so it seemed to work and am trying to keep it up now.
Good luck!