Well not sure where youd get replacement string from, but if youve got the old piece which broke off you can re-use that surely? Youd need to take off the cover to the socket itself and see how the remaining string is held in, and from there you should be able to figure out how to 1. remove the remaining piece and 2. attach the end of the piece which broke off.
Its a good idea if you turn off the lighting at the fuse box before you attempt any of this, and make sure you have adequate light and a safe ladder in place.
Ross, November 2005