The government certainly influences the terms of the BBC's charter (I'm not sure how much, though), which is renewed every ten years. The current charter, for example, which runs from 2007 until 2016, requires that the BBC must do the following:
- Sustain citizenship and civil society;
- Promote education and learning;
- Stimulate creativity and cultural excellence;
- Represent the UK, its nations, regions and communities;
- Bring the UK to the world and the world to the UK;
- Help to deliver to the public the benefit of emerging communications technologies and services, and take a leading role in the switchover to digital television.