Hi Sue. The reason the tap still drips is because the tap seat needs to be reseated to create a seal again, these tap reseaters can be bought from most DIY or plumbers stores. Remove the top as you did for the washer replacement, the reseater is then screwed into place and turned to remove the damaged brass seat until the seat is flat. Renew the washer as well. If the taps are old I suggest replacing them.
Brian, February 2009