"The Chairman and the non-executive members for the nations are appointed by HM The King on the recommendation of Ministers while the other members of the Board are appointed by the BBC through the Board’s Nominations and Governance committee."
"The BBC is primarily funded by a compulsory annual TV license fee paid by UK households."
That's a state media, regardless of what it may view itself as.
Edit: Also, I wasn't wrong about the House of Lord being dictatorial. The things I was wrong about was the complexity of the dictatorship. Instead of it all being chosen by the monarch, some of it is chosen through bribes, some by theocrats and some by politicians. None of the seats are directly chosen by the people, like in a democracy, and that was the whole damn point!