Hello Manana,
I used to live in London pursuing my Master degree. I've visited the campus of UCL and LSE. They're quite close. I lived in the residence offered by my university. To be frank, I'm quite satisfied with both the expense and its neighbourhoods. It's an en-suite located near the Thames River in Southwark, Zone 1. The south bank area is always hustle and bustle and I can promise you can safely hang out with your friends even at 11 pm. I tried to move out of the accomodation my school offered me and I also compared the prices between living outside and living in the accomodation. The fact is choosing the accomodation is much more cheaper and you don't need to worry about all the bills like gas, electricity, house tax and more. Considering you'd like to share a studio with a couple of women, then I suppose the price for each person will be roughly 200 pounds per week and 800 pounds per month. For commute cost, you can apply for a Student Oyster card to gain a certain percentage of discount. I can only remember if you get a student card, you can enjoy a £1.5-2.5 single way by bus. The tube there is quite expensive but sorry I forgot the detailed price (about 4-6 single way? I suppose). When it comes to food, the cost is around £5-15 per meal. But if you choose to have your meal at an exquisite restaurant, then the price will be around £30-80.
It's been quite a while after your last log-in. However, I assume most of the students who're accepted to get a place in UCL might choose to defer their offers. So, I hope my comment can still help you in some way.
All the best,
Felix.