heyy!
I was in the exact same position as you were: I really want to be a journalist, and work in the digital field, but I was really afraid that studying Digital Culture would end up restricting my ability to work in tv or newspapers if i wanted to.
Although the course does sound interesting, I ended up choosing to go for Communication Science at the University of Amsterdam because I feel like it will give me a broader idea of how it's like to work in the media, in general. And, as you said, not studying journalism at undergraduate level doesn't mean I can't get into it afterwards. But, like the one at King's the course I chose is very theoretical, so if you think you would like to learn more about the practical side of journalism right away, then I would say go for the degree at City!