The ISP isn't bothered about the legality of the content in question, that's just a nice cover-up for the real reason: Bandwidth.
Bandwidth costs ISPs money, and with more and more people actually using the Internet to download MP3 music files, Episodes of Lost they missed last week, and sometimes full-length movies, the ISPs are being hit hard with the cost of bandwidth.
New services like BBC iPlayer, Channel 4 OD, and Zattoo.com are costing the ISPs money, and they don't like it. It's very noticeable if you stream a full hours worth on a basic 4mb package with Virgin, after around 35minutes, you'll see the stream buffering. This is where their secret weapon comes into force. Throttling.
If you exceed over X amount of data within the hours of Y to Z, your top speed will be Throttled to A. Meaning, if you're on a 4mb connection and you go over their limits, then your 4mb connection goes down to 0.5mb for a duration of time.
Unlimited, no... in my opinion that is a limit. The courts disagree though.
Fed up?
https://www.bethere.co.uk/ are meant to be good and I don't think they do any traffic shaping/throttling.
I'm moving away from Virgin at the end of next month (I'd have done it already, but we had the BT telephone cable physically removed to make way for our conservatory).