Most site use Flash, and that means using a Flash capable browser like Skyfire or Puffin. Very hit or miss, but some people seem to find them usable.
Most decent streaming is done via apps like Netflix or Hulu Plus. There are other streaming solutions that work using your computer as a server, either for local files or as a VNC solution to view anything on the internet..
And since you are in the UK, I understand the BBC has recently released an app that will stream their shows. I think it is free if you are a subscriber. The rest of us are supposed to get it eventually, but we'll have to pay.
Search the forum for streaming video. You'll find a wealth of information and opinions.