Of course it is state-funded. The state has made a law that requires anybody who wants to own a television to pay money to the BBC.
The BBC is not state funded, state owned and state controlled perhaps - but that's a whole other discussion. Television owners can elect to pay or not pay for a TV License which is what funds the BBC, there is a choice. What is state funded are the 4 million or so licenses which are free to anyone over 75.
> The state has made a law that requires anybody who wants to own a television to pay money to the BBC
Not quite correct. You can own a television and decline to pay the TV license provided you don't watch or record live broadcasts. This means I can watch stuff on iPlayer on my Roku/PC/Android etc and the BBC can't force me to pay a license.
I ditched my TV license back in 2006 for political reasons, I've had a couple of visits from the TV License "enquiry officers" (who are in fact employees of Capita, a public limited company). You don't have to permit TV License staff access to your home or provide them with any personal details. In fact you can permanently deny any TV Licensing representative from setting foot on your property. This is known as "Withdrawing implied right of access" [1][2].
[1]: http://www.tvlicensing.co.uk/about/foi-administering-the-lic...
[2]: http://www.bbctvlicence.com/Withholding%20implied%20right%20...