Hey!
I am a King's student, in the International Relations BA, so I thought I could reply to your question. King's is a university that attracts a lot of studious people, but I have never felt like King's "churns out" the students... Instead, I feel that King's encourages students to do loads of other things beyond studying, like being part of sports team, attending all kinds of different events, and joining fun societies (there are soooo many societies, like a Harry Potter one, a baking one, etc.) There is honestly always something going on, sometimes events related to the studies, but also many other things like the ones I mentioned. I feel like King's definitely want me to do well academically, but also wants me to enjoy my time at university and in London - in a city like London it's hard to only think about the studies!
So, my personal experience is that the atmosphere at King's is about much more than just studying and graduating. If you have the possibility, see if you can attend any of the Open houses that King's have - that might give you an insight to what life at King's is really like.
Hope this helps!
Emelie