Try replacing the internal rubber washer. diferent taps (faucets) have diferent types and sized washers. Turn off water supply,(if safe to do so) ie; water heating system off. Make sure all water drained out of tap, by leaving taps on and opening taps and flushing toilet on upper floors. Dismantle upper end of tap to reveal washer, remove and replace if looks worn /damaged.
Dont forget to switch taps off before turning supply back on. Turn taps on slowly to release air.
Henry Skop.
December 2009