I know most of the forum will say "oh just use an extension cord" but remember that they do periodically cause fires or electrocutions when abused in this way. I'm not saying don't do it ever under any circumstances, necessarily; but I *am* saying don't do it *lightly*.
So, I mean, why do you want electric light out there?
If you are just concerned about being able to check on the chickens after dark, best plan is to get yourself a $15 headlamp. Great things, useful for a lot more than checking chickens.
If winter laying is an issue, then at high latitudes (e.g. the UK, which is the original poster's location) you may need to choose between either a) accept a drop or temporary cessation in laying, or b) run an extension cord as safely as possible and hope for the best, c) run PROPER electric service out there, or d) fiddle around getting together the components to put a solar cell on a controller and battery with a DC timer on it [which BYCers keep *talking* about but I am not sure I have actually seen a working example posted yet]. At lower latitudes (e.g. amydzek is in Florida) you can often get away with just installing a shrewdly-chosen solar patio/driveway light, so that the panel is on the outside of the coop on the S side and the actual light part is on the inside of the coop. The battery will gradually dim out as the night wears on but if you are playing your cards right it can give you enough extra hours of light to add up to a 14 hr day for the chickens.
For laying purposes, all you really need is enough light to read a newspaper by without squinting unduly, at chicken level that is. In an 8x8 coop that may be a 40 or 60w bulb, or so, depending on ceiling height and what color things are painted in there.
For those in cold climates, running a heated waterer or heated waterer base is a whole nother thing and really is best done by running proper electric service.
GOod luck, have fun,
Pat
