Universities in London usually claim that living costs for students are approx £1000/month, i.e. 12K per annum. Now of course that's a completely subjective matter and depends on what kind of lifestyle one lives in London, but it's a pretty good average.
Housing is very expensive, particularly in West London, where Imperial is - depends on location, room size etc. of course, but you would be looking at anything between £90-150/week. Transport is approx. £25/week, though cycling is of course free
All in all, you could if you really stretch it, bring your living costs down to around £700 (I know quite a few people who live on less), though around £1000 should be enough to worry less about bills.
Good luck!