@Bubble and all others saying get a job... there are a lot of people who HAVE full time jobs and still DON'T have a lot of cash!
The assumption that because one works means you have money severely incorrect not to mention judgemental! Of course these people are going to get a sodding job, it still doesn't mean they will have cash left over to see the place! My sister has a job but doesn't earn enough to live the life of riley! She has fun but doesn't mean she has money to burn people!
Anyway to the asker:
You CAN easily survive in London with not much cash (Most of us do!) Obviously touristy areas will be more expensive for food and what not, but most of us don't shop in those places! Asda, Tesco, LidL, Morrisons etc etc are good supermarkets (although I use sainsburys and also their basic/value ranges) Learn to budget each week for food, write down meals for every day and then mix and match the value/basic ranges with brands. I use basic ranges for things like tinned tomatoes etc so that I can then afford the nicer things! There are lots of pound shops/value shops in London (I like Wilkinsons) so you can easily buy pots and pans, stationary, household items and good for cheap prices. Nothing fancy, but does the job! Shop around, look for coupons in supermarket magazines!
There is also Freegle/Freecycle groups where you can ask for free items and give away your old unwanted items too. There is also the Gumtree for freebies and low cost items (manyAussiess and saffas use this when going home so watch out for free items to take that day!)
There are TONS of free or low cost things to do and places to visit around London. BUY Time out if you can or the best bet, is to get the free TNT Magazine on a Monday/Tues outside tube stations.
Great tips,trips, news etc for saffas,Aussies and New Zealanders and everyone else who like me enjoy reading it! They list gigs etc and list freebies as well and outings on the cheap.
London is FULL of things to do and you don't have to spend money. The tube can be expensive even with a one day travel card, so hop on a bus!
Make up some sandwiches before you go, buy a pack of cheap drinks or soda/pop to bring with you all on your outings so that you don't have to spend money on expensive central London hot spots!
(also gives you a little extra to have a nice coffee or hot chocolate or something nice on your way home if you wish!) Also try to get hold of the metro, because very often they have £1.99 burger and chips MacDonald's deals which i have used when we are on a trip out! Does the job!
On a night out, just buy some cheap drink in the supermarket and start your night at home, then go to your club or gig! Go there and back by bus, it's cheaper!
Find a decent flatshare in a cheaper area (tons of saffas for example in East London, my sister lives in one lol) Make sure you split the bills, keep lights off when not in use, wrap up instead of whacking on the heat full throttle, shop around for the best energy tariffs and give in gas metre readings instead of letting them estimate your usage.
There are many many Londoners, inc students, and visitors who live on low wages AND STILL have a great time! London is FULL to the brim of cheap places, free places and fun places. London doesn't have to be expensive, it just takes a little working out! :0)
Hope you have fun!