But that isn't the issue and is purely tangential.
There go those ‘tanned genitals’ again ~ they just keep popping up in all sorts of conversations!
As it happens, the BBC isn't government-funded either, other than a very small Foreign Office grant to the BBC World Service (radio). The TV Licence Fee which funds the BBC, although collected by a statutory agency, is not subject to variation by government decision, isn't part of the government's budget, and the government has no say in how the BBC chooses to spend it. The principle of complete independence of the BBC from government control was firmly established in the 1920s and 30s by its first Director-General, John Reeth, and has been fiercely upheld since (much to the occasional regret of all successive governments, of whatever party, when anti-government views are broadcast). In wartime conditions, Churchill did briefly toy with the possibility of bringing the BBC under direct government control, but wisely thought better of the idea.