There are lots of TV channels that offer live streams of their broadcast programs off of their web sites. This includes the BBC.
"Live TV" means that it is possible to watch it over the Internet while it is still being broadcast. An example of "Live" would be a 30 minute sit-com that is available over the internet 20 minutes after it starts on a broadcast medium (overlapping by 10 minutes). For things like football matches, this means that it must not be available on-line before the broadcast program finishes, i.e. at least 1:45 (and maybe longer) after the match starts.
The distinction about whether you do watch live TV online or not is very blurred. Iplayer, for example, allows both archived (catch-up) and Live, so how to you prove that your use of Iplayer is only for catch-up. It all looks a bit murky to me.
I wonder if the TV licensing people are able to get a court order to request your browsing history from your ISP?
I still wonder whether an analogue TV without a digital tuner still counts as TV receiving equipment. In my view, it shouldn't.