Did you miss this:
> UK Government cannot determine its agenda or directly influence its funding.
> The BBC will regularly criticise the government
The funding is set for a 10 year cycle, beyond the scope of any individual government specifically to protect the BBC from editorial interference by the government. That’s why it’s a publicly funded broadcaster, not “state media.”
The onus is now on you and the OP to prove your claim that the BBC is state media.
When I say state media I mean media that exists as a part of the state. Like when it's funded by the state or the state has some other kind of influence over it.