Don't listen to LutherVan when it comes to his weird ranking of "international prestige", he is repeating that nonsense in other threads. There is no elite of 9 universities with higher international prestige than others, at most 2 (Oxford and Cambridge).
Now, if you worry about getting internships easier at King's - don't! Warwick is one of the very top targeted universities in the UK, loads of companies come here to get students. We don't live in an age anymore where distance from a place matters as much anymore, and I reckon the internship possibilities are at the very least as good as KCL, probably better as Warwick is more targeted by banks (not sure if that's your interest though).
When it comes to social life, it's what you make of it, but that's true at any university. If you stay in your room, you will have a poor social life, and being in London will not change that. At Warwick, have the biggest student union in the country, with a huge number of societies for basically anything; same for sport clubs. Sport facilities are many and of high quality. The Student Union is a bit boring when it comes to nights out, but many nights are still very popular, especially among first years. There are plenty of bars and pubs around campus and close to it too. That said, many people do venture out to Leamington to go out, and there are special buses that take you right there, so that shouldn't be much of a problem. We also have 2 cinemas, an art center, many cafes, etc. I doubt you will get bored, unless you come here thinking that you will and never venture out of your room.