You might think the BBC is a leftist far-liberal website, but the BBC is actually the British state broadcaster. It's positions are quite statist and monarchist, neither of which fits any traditional "leftist" position. The rest of your evaluation is just a diagnosis of your politics.
The BBC ids not what most people would consider to be a state broadcaster. It has a Royal Charter, which makes it independent of the government of the day. It is financed entirely by an annual licence fee levied on all households with a television receiver.
The Royal Charter is the constitutional basis for the BBC. It sets out the BBC’s Object, Mission and Public Purposes. It must:
1. provide impartial news and information to help people understand and engage with the world around them
2. support learning for people of all ages
3. show the most creative, highest quality and distinctive output and services
4. reflect, represent and serve the diverse communities of all of the United Kingdom’s nations and regions and, in doing so, support the creative economy across the United Kingdom
5. reflect the United Kingdom, its culture and values to the world
This last one is defined as follows:
The BBC should provide high-quality news coverage to international audiences, firmly based on British values of accuracy, impartiality, and fairness. Its international services should put the United Kingdom in a world context, aiding understanding of the United Kingdom as a whole, including its nations and regions where appropriate. It should ensure that it produces output and services which will be enjoyed by people in the United Kingdom and globally.
I hope this is useful.