That may be your belief but there are plenty of people who think otherwise. http://biasedbbc.org/
What they don't do is run directly biased stories; they're "neutral" in the content they put out, and any perceived bias is the result of their tendency to hold off on running boat-rocking stories. You could easily argue that this is a bias in itself, but it's not a partisan bias and it's hard to see how they could do this differently; it comes from their entirely legitimate fear that if they annoy any current government too much then they might lose the license fee advantage.