We pay the licence fee to fund the BBC. They make some amazing documentaries (Planet Earth, Blue Planet etc). They also have radio stations, all advert free. Being advert free is rare these days.
Personally I think that it should be organized like a tax nonetheless, because if a public broadcaster is a benefit to society, it's a benefit to those who watch just as much as to those who don't watch, similar to how those who don't enter medical school will still enjoy the availability of doctors. A precedence exists, in Germany the Finanzamt is happily collecting a tax-like thing on behalf of the established churches from their members, without that ever having led anyone to suggest that the churches were controlled by the government. The investure controversy isn't exactly still lingering.
So the tax lives on in this archaic form instead and every now and then when the Tories are in power they try and defund or threaten the BBC somehow. Usually within a year of getting elected, and then there's a backlash and they have to back down.
The latest wheeze was to force the BBC to get pensioners to pay, and they managed to pull it off by getting the public to blame the BBC instead of the government.
https://en.wikipedia.org/wiki/Channel_4
Although they're mostly funded by ads and selling their programming now.
Channel 4 is a bit of an odd one, as it's publically owned but not publically funded.