You'll probably find, if you take it apart, that the washer itself has parted company with the tap insert itself...you'll have to isolate the water supply, take the tap top off (usually just a single screw under a cover) and unscrew the tap insert with an adjustable spanner. The washer should be on the end of the insert (often a push fit, but sometimes held on with a small nut) - or it may be floating about in the tap unit itself. You may be able to get a new insert from the likes of B&Q but take the old one with you as there are a few different types. Failing that, you could just replace the washer.
John
January 2008