you could power thecircuit via a transformer, or i suppose it could be powered from the mains if rectified as long as componets with suitable values were chosen, the variable resistor might pose a problem, if the variable resistor had a metal base it would have to be earthed and the circuit placed in a plastic box(or earthed metal one). The light would not either be on or off, it will illuminate proportionally to the darkness.
the circuit below will be definite on or off as it uses a relay, this is one way of doing what you require another is without the transformer(the bottom schematic) personally i would use the one with the transformer.
hope this helps?