Overall, over the decades, I find the Beeb make a reasonable fist of being unbiased. With the occasional ludicrous attempt to balance by allowing a fringe a voice. Some instances of which have been apologised for.
When an opposition gets into power they still complain, no matter who Paxman or Humphries has had a pop at lately. I think any preferences of the types of stories they run are a reflection of the times, and perhaps the sort of people who choose to go into the media rather than any overt bias. Thus for some they are viewed as biased centrist or centre left in always seeking balance.