I'll be going to King's this year, as a mature home student studying Computer Science at the Strand Campus (which I believe is also the campus for Ancient History). When I visited the campus, it seemed safe enough. It's right in the heart of London, with the Royal Courts of Justice just a few hundred meters away. I can't see it being too dangerous a place since it's so bustling/busy! I personally love the location, and can't wait to move to halls.
Just to add a little credence to my opinion, I'm not speaking just as a future student/resident of the area, but as someone whose work used to take them to the courts on a semi-regular basis. I used to get off at the same station as I would need to for the campus (Temple station), and in all my time there, I never experienced or witnessed a bad incident.
Hope that helps.