BBC as a news source whilst far from perfect is still very much respected worldwide and considered one of the most reliable news sources in the world, most people who moan about them being absolutely terrible tend to be on the extreme ends of both the right and left. They are either too lefty because they push social justice issues or they are too right because Kuensberg loves Borris or whatever.
When you have both sides saying they are too right/left wing then that's usually a hint that they aren't quite as bad/biased as both sides suggest.