Possibly it is the galnd that is leaking, follow the instructions given in the link. http://www.ultimatehandyman.co.uk/stop_tap/re_Packing_a_stop_tap_gland.htm
There may be a domed chrome shield covering the gland. The shield unscews (anti clockwise) or merely pulls off. They are usually hand tight but may need a pair of footprint pliers or similar to shift it because of the gunk that collects. Place a rag or sock on the shield to stop the chrome from being scratched. good luck. Hope you dont drown.
The Drip
December 2010