Not a student, but I'm living in a 1 bed flat in Chiswick. 1 bed flat. £27/mo Electric, £24/mo Water, £45/week shopping for 2.
For a student, check out spareroom.co.uk or gumtree to find a room that you can rent in a house share, it'll be your cheapest option. My friend rents a room in Hammersmith for £600 inclusive of bills. It's in zone 2, so if you're willing to live further out, it could be much cheaper.