BBC owned by the Government, that's a new one on me.
The BBC is funded by the public via the license fee, it has a charter to cater for all tastes (and that includes Sci-Fi fans).
Actually, from a technical POV, the license fee is considered a tax. It is paid into the Government's Consolidated Fund, before a convention has the Department for Culture, Media and Sport voting to hand it to the BBC for their own use. This is why the BBC have to negotiate with the Government of the day in regard to license fee increases.