OP the student loan is what the government 'thinks' a student needs to live on. So whether you're form the UK or not is irrelevant.
The max maintenance loan for a student living in London is 13,022, divided by 9 month academic year that's about 1.5K a month.
There's plenty of information online if you google 'London living expenses' but really it's a matter of how far you go. A PP mentioned students meeting for 'lunches and coffees' - not really, if you're skint. London has plenty of free things to do anyway. People load up on pre-drinks before going out, so they have to spend less.
I don't know where you're from but food in the U.K is very cheap, £30 -£40 a week is enough. London is full of Asian restaurants with big portions. I used to get a main then make rice, that was enough for 3 days. Clothes etc are really cheap especially if you're savvy with charity shops.
I also worked as casual staff, we got fed and sometimes got food to take home too :) so that kept costs down! I got tips and stuff so that would good. But as PP mentioned tutoring, or working at the uni itself pays more.
There are also student discount apps like Save the Student, Unidays for example.