Change the washer anyway.
Sometimes the seat corrodes and little pits form allowing water through. You can get a "tap re-seating tool" that grinds the seat to make it flat again...
http://www.plumbworld.co.uk/tap-reseating-tools-239-0000Be aware that removing metal from the seat using this tool sometimes exposes tiny bubbles and fissures formed during the casting process which makes the problem worse. So try a new washer first and be prepared to replace the whole tap if grinding the seat fails.