It's called a PC. and cable or Broadband Internet with TV
Virgin Media do it, so does TalkTalk ( http://www.talktalk.co.uk/products/tv/index-tv.html?code=ZZ-NL-12XA&cookie_check=1 )
Your own broadband provider may do it.
There's always BBC catchup (and the ITV/Channel 4 and Channel 5 equivalets as well)
Jonno
May 2010