the amount of time and money required to properly refinish a guitar (especially with a set neck) makes it kind of redundant to get a 2nd hand les paul to have it done on in the first place. save up a bit more and get a new black one from the get go. i wouldn't consider a refinish unless it was a really rare vintage guitar or something with lots of sentimental value that somehow got damaged.
from what i can find through google you're looking at a good $500 US and up for a strip and refinish.
as for places to find a 2nd hand guitar.
london musical instruments classifieds - craigslist
Electric guitar for sale, London UK - Cheap guitars online
it's not hard to refine the searches on those sites for cities closer to where you are. you could always try leaving a note on the bulletin boards at your local music shops letting people know you're in the market for a used LP.