It really depends on the accommodation. I know about Avery Hill and Medway campuses, but the Greenwich main campus (I think) is different, but I imagine it would work similarly. I could be wrong though.
For Medway and Avery Hill:
Streaming: fine, most of the times.
Torrenting: Not allowed, and they say that if you are caught doing it then they will take away your internet. However, I know a lot of people who got away with it.
Gaming: As a heavy duty gamer, I found that while it's possible to play online games, the connection is honorific bad. There's no steady stream - you are guaranteed to be cut out from your game about 2 times per minute, and it can become as bad as more then 10 per minute at peak times. It connects right back almost straight away, but that second that you miss could mean the whole game. It takes away ALL the fun from playing online...
As I said, I don't know about the main campus. I hope it isn't the same as Avery Hill or Medway.