I think the issue people have with the BBC are that it is very much controlled by the government/elite. This is the case for most British media though - compare

I think the issue people have with the BBC are that it is very much controlled by the government/elite. This is the case for most British media though - compared to the US there isn't anywhere near the level of independence. (Also the BBC isn't currently funded by tax payers, but most likely would be if the license fee were abolished https://www.bbc.com/aboutthebbc/governance/licencefee https://www.bbc.com/aboutthebbc/governance/licencefee)