The BBC does better than others, but I agree - there really as no such thing as unbiased media, and "better than others" is still no where near good enough.
Though with all media outlets, it goes deeper than just how they report on stories - anyone with an even slightly independent mind can at least detect the bias, whichever direction it goes. The really insidious thing right now is the selection of the stories to tell, period. It's what they choose not to report on that is often the most divisive - because instead of multiple biased takes to pick through, many people aren't hearing anything about it at all - and if they do come across it - "oh, that's from a (insert your bias) outlet" and it's completely dismissed.
It's happening across the board across the entire political spectrum, and it's why people feel like they live in two different worlds, because both are at the mercy of biased news. And then you have those of us who live in yet another third world - where we look at both worlds that are full of bias, think both are crazy in their own ways, and are largely just stepping back because, frankly, it's a full time occupation to keep up with it all. There is so much garbage everywhere, almost no one is addressing the actual day to day problems of most peoples lives, it's easier just to let them duke it out because unless you are lockstep 100% with either one, it's generally a futile waste of time as neither side wants anyone who isn't 100% committed to their ideology.