You can get a 12v DC to 230v AC power adaptor in places like DIY and car accessory stores for around £20 i think which you can then plug the router PSU into.
Depending on the router you might be able to connect directly to car somehow. For example looking at Netgear PSU the rating is 12V DC 1 amp, which in theory a car battery could supply directly. Otherwise a cheap mains adaptor and then the usual PSU would work great.
Otherwise see if you can borrow or look for a cheap UPS. These are designed to keep a desk top PC running for a good few minutes so a router should run for ages.
*EDIT*
what about ampage though? (Im not a sparky lol)
Me neither. I seem to use that "compare electricity to water" idea. Volts is the size of the pipe and amps is the "pressure". Volts enables more current to be supplied, but the amps is the measure of current passing through so to speak.
Then watts is a measure of energy or something and is volts x amps, but when you monitor the power consumption of a 12V 1 amp router it is not actually 12 watts. I guess again this is the maximum power that can be supplied using the power supply and that the actual supply is dynamic to the requirements of the device.
(Please correct me if I am wrong before I do anything silly...)