There are those on the right who wish to defund the BBC. Many, both on the left and the right consider the BBC to be biased. It is hard for any news organisation to remain impartial, and while the BBC does engage in propaganda at times, it is less partial to this than other parts of the media which tend to parrot the messages of the right.
The BBC is a way of projecting soft power. The World Service is listened to across the globe and has been important in letting those in nations where the media is very controlled, another perspective on life. Cuts mean people are then listening to the media that states that Everything is Awesome, even when it is not. Cuts have been made in the past, and that means the voice of our nation is not as loud.
When people watch shows like Dr Who, they view the UK in a better light. After Brexit that is even more important.