It's anyone with a set now? I spent about 1.5 years in the U.K. in '91 - '92, and it was anyone with an antenna then. I had to pay the bill twice, as my stay spanned two billing periods. Oh, well, at least I didn't get billed for Maggie's Poll Tax. Some of the people working with me did, and they had a tough time proving that they were U.S. citizens.
It's actually per household/residence/business address - though there are reduced rates for multi-occupancy premises such as nursing homes and similar. It still stinks but there is talk of phasing it out by around 2012. Mind you, that's not altrusim on the part of the BBC, they just recognise that, by then, broadband reception will be so widespread that most households will be viewing via the net. In order to capture that, they'll need new legislation and it wouldn't have a cat in hell's chance of getting through Parliament.
As to the dreaded poll tax - it's gone. That issue was so unpopular and evoked so much public dissent (indeed riots) that they had to scrap it and go back to the old city council tax. It was also the only issue in recent years in which we Brits actually got so pi**ed at our government, we came close to displaying emotion ;-)