How do Phd student survive in universities situated in central london? eg Imperial college or UCL. I would like to apply for a phd there but the living expenses in london city is a real deterence.

I'm doing a PhD at KCL - you're right, London is expensive, but it’s a great place to live! You need to check how likely you are to get a grant and how much it's likely to be and also how often you have to be in college. Depending on how often you have to be in, you don’t necessarily have to live too centrally. You’d pay much less rent on the outskirts or even in Herts/Bucks and could travel in by train.

I'm doing a PhD at Imperial (2nd year) and have recently bought a house with my better half in the outskirts. So anything is possible! It is very expensive, but I agree with luci. Find out how often you have to be in college (mine is very flexible) and see if there are any days you can work at home (such as when you are just reading). To cut down on costs you could try cycling in to work (or running, like I do).