A couple of years ago I took an overseas friend and her son around several London Universities. Self guided tours are usually published on the website, but Universites were all clearly used to people just turning up, and the son had a long chat with the administrators team. He must have been impressed as he is studying there now.
You need to go. KCL is amazingly diverse. The MN obsessions about rich and poor, private and state are not as divisive when your coursemates come from all around the globe. It is difficult if you are more comfortable with people from similar backgrounds, less of a problem if you are happy to take people as you find them.
Living as a student in London is a great was of experiencing the City. Lots is free, but equally lots is expensive. It depends what you like and how organised you are. London nightclubs are pricey, but student discos aren't. There are free concerts, cheap theatre tickets, museums, talks etc. Lots in London can be reached by walking, bus or bike. Eating out is expensive but ethnic food can be good and cheap. And so on.
KCL (Strand Poly as it was known by the people across the road) will be a challenge, but can be a rewarding one. You need to see to decide.