I’m assuming this question relates to the BBC’s journalism, as opposed to its cultural output, and on that score the evidence from decades of research is very clear. It shows that BBC journalism is overwhelmingly orientated towards ‘establishment’ sources, that is to say powerful people and institutions. Broadly speaking, studies suggest that governments are the most significant sources in BBC news, with 10 Downing Street and then Cabinet Ministers at the top of a news hierarchy. They are followed by the official opposition, other Westminster sources, and then other people and institutions with significant influence in the policy world, such as journalists, representatives of business, private think tanks (close to business and the political elite), and so on. Charities and trade unions also feature, as do members of the public, but generally only as contributors to discussions, rarely able to drive the news agenda. In economics and business reporting, private companies are significant news sources, along with politicians and official statistics.
So the BBC overwhelmingly reflects the views of the Establishment. Whether it does this too much is really a question of opinion. Some might consider it appropriate that the BBC largely defers to the powerful in its reporting. To me it seems at odds with its commitment to reflecting a plurality of views in society and it is certainly problematic when you see a marked divergence of opinion between the Establishment and the public.
The picture, it should be said, is somewhat complicated by the fact that establishment sources don’t always speak with one voice. Even within the government different people and departments have distinct interests, and in formal politics there is a competitiveness built into the system and different parties and party factions represent different interests and adopt different strategies. This element of contestation within the Establishment allows BBC journalists to question authority to some extent, whilst not diverging from broader elite opinion, and to square the reality of BBC reporting with some rather spurious assumptions about the social role of journalists.
You can listen to a podcast about the new book "The BBC: Myth of a Public Service" here.