BBC - BBC iPlayer - Help - Home
As far as I have ever been aware you only need a license if you are streaming live channels, whereas BBC iPlayer is delayed by a particular amount of time.
We have a tv license though, I just don't contribute because I don't use the living room or the TV.
EDIT: Thanks for your concern though, but obviously I checked before I watch stuff
I don't want to have a criminal record being a law student