Johann Hari seems to think so.
I'm inclined to agree, the BBC is very vulnerable to reports in the less principled media of accusations of left-wing bias. This is because much of that media is controleld by right-wing oligarchs keen to push their own conservative agenda. It could reasonably be argued that if the BBC spent all its time fighting unwarranted accusations of liberal bias then it wouldn't have a lot of time left to report the news and make programs.
The problem is that this argument negates the BBC's own reason for existing. Yes, they are there to make TV and radio programs to entertain but the BBC was created to report news objectively. The stated mission of the BBC is "to inform, educate and entertain".
Read the article, see what you think. I'm with Johann on this one.