It's not as tightly controlled from the top as RT for sure, but the BBC is definitely used as propaganda for the state. You might agree with it more, but it's presenting the state as legitimate: everything related to the crown, to the _former_ colonies, to the government, and so on, is presented working on the assumption that things are mostly as they should be. This is propaganda for the state. To be clear, I'm not saying if I think this is good or bad, just that I think it's arguably true.
Aren't you then saying that it's impossible for anyone to hold a sincere view that "the state is legitimate"? By definition you're defining any such view as propaganda. All propagandists believe the state is legitimate, but not all people that believe the state is legitimate are propagandists.
A person can hold any view they want (organizations such as the BBC aren't people, and they can't really "hold" views, but I digress). I think that if they spread that view, when paid/supported/otherwise made to exist by whatever entity that view is benefitting, it's advertising. And if it's political in nature, then it's propaganda. The British state funds the BBC and relies on it to show the world what the UK is all about, and to me, that's qualifies as propaganda.
