This really depends (final year here).
Anywhere a studio is going to be expensive, if you have the money great but most people get by by being in flat shares which is far cheaper, normally with other medics/imperial students.
In terms of where. For 2nd year you are based mainly at charing cross hospital but also South ken. Well was when I did it. This means most people live around charing cross so hammersmith/fulham and a few in shapers bush. Most seem to stay there. I moved further out to acton for the last 3 years because it was cheaper and not that much further from central timewise (if you pick somewhere with good tube links). Plus nearer to the further out hospitals!