@ Bugbear...
The bit you quote is, I think, deliberately misleading. It's par for the course regarding the Licensing office, as they like to frighten people.
The law is reasonably clear, but annoying:
1. You need a licence to receive ANY TV programmes from any broadcasting organisation at the same time as they are broadcast. I don't think the internet aspect of this has yet been tested in court, but IIRC, it's covered in the most recent amendment to the Wireless Telegraphy Act.
2. You do NOT need a licence to own, install or use a TV, unless you are doing (1) above. The licensing authority has lost in court on this several times. This includes things like creating your own modulated TV signal for local distribution of video material (by wires), using a video player connected to a TV, and so on.
3. You do NOT need a licence to own, install or use a computer, unless you are doing (1) above. Even then, it's not been tested in court, as far as I know, and the area is a minefield, for example receiving streaming media from offshore, etc.
4. You do need a licence for recording anything off-air to any sort of recorder. This means time-shifting, etc.
5. You theoretically do need a licence for mobile devices receiving 'live' streamed media, or for portable TV receivers, terrestrial or satellite. If you already have a licence for home, this is usually treated by the licensing authority as covering mobile appliances.
6. Other grey areas include students in term-time accommodation (it used to be that parents' licence covered them, but I'm not sure now), and arrangements for hotel accommodation (one licence per room would be rather expensive!). IIRC, each holiday cottage/apartment needs its own licence.
7. So far, any on-demand internet video distribution is licence-exempt (youTube, BBC iPlayer repeats, etc.). Having been daft enough to create this loophole by putting stuff on the Web, the BBC is now trying to staunch the wound with a "commercial" version of iPlayer available on subscription to overseas customers, but it's lacking the 'live' streams.
I'm not sure about the present status of the inspectors' powers of entry to premises. It's certainly true they didn't used to have authority to demand entry, however one of the last acts of the last government was to give a wide range of entities powers of entry, including local authorities (on various pretexts), and I think the TV Licensing Authority too. Personally, I'd still refuse them!
It has never been the case that the licence is for ownership or use of a TV, as such, but see (1) above.
I have scanned the most recent WTA amendment, which sort-of addresses t'interwebthingy, but still isn't completely clear. Technology is moving too fast for legislation to keep up!
I write as an ex-BBC-droid (years back). I am NOT a lawyer. There were supposed to be only two guaranteed ways to get sacked - insult the DG's wife (per Kenny Everett), or fail to pay for your TV licence. I never got the chance to do the former, and only owned a TV for one year during my career (got enough of it at work!).
Cheers,
E.
PS: Other oddities include the fact that there is still a black-and-white licence, and that receiving mute colour pictures doesn't count as watching colour TV! Again, this last one may have fallen by the wayside now.