I've just moved into my first place, and for reasons I do not condone or recommend I don't have any method of refrigeration right now. Luckily I now live very close to shops, so it isn't a big deal, but it made me think: if I really had to, what would be the most efficient way to keep food cool without using any electrical (or any other means which would be impractical) method of refrigeration?
There are cooler boxes . Have a look at http://www.minicoolers.co.uk/ . I had to make do with one such when my fridge went on the blink till it was repaired. They are as good in keeping food as ice boxes used to be. They just use the normal mains. If you have no electricity you could get one without used for picnics and buy ice every day to keep things cool.
Pasteurized food is preserved for long time (boiled soup without opening the pan, for example).
Wrapping your food in a moist towel will cool it due to water evaporation. You can use fan to enhance this effect.
For temperatures below zero, ask for some ice in the shop and mix it with salt.