It Exists.
Apparently as the government pays money into broadcasting, they have a specific tax based on if you watch TV or not, to help support it. Might be their equivalent to a cable bill? But yeah, that shit's real yo.

It keeps the BBC advertising free for one.

True. Although Finland dropped that from 2013 onwards, now it's taken directly from taxes. Before that I didn't pay my TV license and I regularly got these letters too. Finnish letters were more polite though. You didn't have to prove you didn't have a TV, only if the inspector caught you actually having one you had to pay. The Brits seem to be very militant about this, this letter is actually little shocking for me too.

Yes. Basically you need a license to own a TV. They send those letters out automatically to any addresses without a TV. Eventually they send someone around to check you don't own one. If they find you have a television they make you sign up for a license or take your set away.

I don't actually mind it. It means the BBC can be more experimental and take risks, as they're not tied to advertising revenue.

I still haven't forgiven the BBC for cancelling Being Human though.