These tables are very hardly so if you can't do this yourself your local french polisher should be able to help. No more the £100 for the whole table to I recon.
If you want to do it yourself get some very fine sand paper. wrap this around a block of wood the size of your palm and sand the surface in straught line with the grain. Don't rub too hard and don't be tempted to rub hard were the rings are. Wipe the surface over with clean water, this should darken the same tone all over the top. If it doesn't wait for it to dry and rub some more around where the water didn't sink in as much.
When the table is all the same tone apply furniture oil, something like danish oil. Apply thin coat once a week till you are happy with the finish. Don't cover the table or put anything on it during this time or for another month after finished.
Never use spray polish on this type of furniture just a damp shammy.
007
February 2008