Hey!
I'm a KCL alumna, having done my BA and my MA there in the History Department, which I loved.
Over the years, I've gone back and forth on my opinion of KCL and, having been part of three departments at one point or another owing to my changing course in my first year as an undergrad, my opinion of the university on the other side of it is generally very positive. I think it varies a lot depending a) on your department and b) on how much effort you are willing to put into your experience there.
Positives first...
I loved the content of my BA and my MA and that carried me through the whole experience there.
It's great to be near to museums and the cultural wonders that London has to offer. I love London and it's great to have the time as a student to get to know it. This is a life skill in and of itself!
In my second year, I considered a legal career and being in central London was extremely useful, as I knew the city well and was able to go to events held by law firms easily. Learning to navigate London is also a skill in itself and you will definitely learn it at KCL!
I have always had very positive experiences with lecturers, who always made time for me and were generally really lovely people, but I know that this varies by department culture and the individual academics themselves. I have friends who did War Studies who struggled with the department culture, for instance, but I always heard good things about Biomed, for what it's worth.
Now to the negatives...
I lived at home and sometimes struggled to maintain a good social life, which only really came into its own in my MA where I met more like-minded people. On my first course, which was joint-honours, I *really* struggled socially as it was hard to make meaningful connections with people and I became quite depressed at this time. I hated my halls (Great Dover Street - which they have since re-decorated) and wasn't very keen on my flatmates (nothing against them - they were just very different to me), plus I had an awful lot going on at home as my dad was dying of cancer at the time. I also really hated the courses I was on which didn't help! My experience at KCL changed completely when I was on the 'right' course for me.
London is more expensive, there's no getting around that. I worked part-time through my degrees and managed fine, getting a first and then a distinction. I know people who worked a LOT more than I did and still came out with good 2:1s. Being in London, there are plenty of great part-time jobs that can work around a student schedule. I'm also lucky to have been able to live at home with a supportive mother, so there's that to bear in mind.
When I joined KCL, they had a 'London is your campus' campaign going on. This is just ridiculous. London is such a big city and the individual KCL locations are too dispersed for there to be a campus feeling. I was based at Strand and only went to Guy's for certain career/extra-curricular activities a few times.
And, finally, down to your personal input into your university experience...
University is what you make of it, ultimately. If you put in little effort into your experience (be it academic, social, career, or anything else), you will get little out of it. Trust me on this: I learnt it the hard way. Maybe if I'd have been more interested in societies and activities, I'd have found friends more easily on my first course. If you think you'll be happy and more productive at King's, then go to King's. If you think you'll be better served at Warwick, then go there. There's no typical experience of any university, as other posters have pointed out here, so (in spite of spending time writing this post, haha!) I wouldn't read too much into other people's experiences at either KCL or Warwick. It's your experience and it's up to you to determine what that means.
Hope this helps and best of luck.