Not much help but since we're talking rent prices.... Back in 2000 my future wife and I moved to London for our postgraduate studies. After much consideration we decided to go the expensive route and rented a room in a flat that we shared with the owner. It was £200 a week, in Kensington, couple of buildings down Earl's Court from the tube station.
Sounded (still does) expensive, but that and the telephone were all the expenses we had to pay. Factor in we would walk to our college (RCM, right behind Royal Albert Hall), and it was more than worth it. Plus, it gave us three huge benefits. Struck a solid friendship with the owner, still friends to this day; we were the happiest we've ever been in that room, by ourselves; we absolutely loved London, still do, contrary to most of our pals who ended up loathing it due to having to commute 40' daily, living in a miserable college hall.
London is absolutely worth it, 100%. That much I can guarantee. However, I am in no position to offer further advice.