Social life as a student in London?

I recently received offers from KCL and UCL for Physics BSc. I love London as a city and have always loved being in big cities. I could definitely see myself living there and am used to living in a busy city like London, so I really don’t think this would be a problem for me.
What I am worried about is what the social life is like amongst students in London. From what I’ve heard, it seems that it’s a place where it’s hard to be social with lots of other students, partially due to the lack of campuses and the distances that separates different uni buildings or accomodations. People also tend to describe the London student community «clique-y» because of the many international students that often befriend only people that share their nationality, or that the Londoners often have well established friend groups and therefore don’t have the need to socialize with new people. I have also heard that the high costs of everything makes the students not afford to go out as much as in other smaller cities, and that you’d also have to plan ahead much more as many places often are overbooked.
London is obviously not a «student city», so I get that it will differ from the really small towns with dominating student populations. But is the social scene for students really this bad in London though, or have people just been exaggerating to me? Are the student unions of KCL and UCL active? Are there any organized events that people actually go to for students? Are people open to making new friends? I would really love to move to London but am super scared that I will be disappointed if there is no «student life»…