“The bbc” is a large organisation with many reporters and editors.

Those reporters and editors put out biased content from the left and right.

There are good arguments that the BBC do not criticise the current government and some people take that to mean that they support the government. That is exacerbated by the fact that David Cameron appointed prominent Conservatives to directorial roles in the BBC.[0]

But yes, the news they put out is not unbiased- it’s just that they have bias in all directions depending on who is writing and editing.

[0]: https://www.ft.com/content/7ba884c2-176d-11e6-b197-a4af20d55...