The simple, and very reasonable, logic is that since the BBC is "The British Broadcasting Corporation" funded and indirectly controlled by "the state" it is broadly supportive of the elected government because that government democratically represents the will of the people. Because it is "the government" of the nation! The only government there is! At the same time, it does not hesitate to report and analyse hard news that puts the government in a bad light. I would hope it will be equally objective with regard to the opposition, or any other political party or movement.
As has already been said, there will inevitably be a difference of opinion as to its objectivity between the Left and the Right, which are themselves subjective positions.
On another tack, it seems to me, as only a poor foreigner, that the importance, in the world, of what British government and opposition leaders do or say is greatly exaggerated in many British minds. The only news stories regarding UK politics I've seen in the Italian papers over the past few weeks have been about "you-know-what."
