My family has a timeshare flat available for one week in late 2005 (I
believe we can take our week any week in Oct, Nov, or Dec) that is
located adjacent to Sloane Square in Central London, right near the
tube. I have heard/read there are groups/websites/etc where people
trade their week timeshares for other timeshares in various locations
(Paris, Barcelona, New York, etc) and was curious as to the names of
the sites and which are most reputable. 

Preferably, I would not like to pay a finder's fee, but would be
willing to do so if that were the only possible way.

Here is a free database for timeshare exchanges:

http://www.tug2.net/ads/directdb.html