Older style taps are fitted with a gland nut holding in watertight packing around the spindle. These taps may leak between the spindle and the cover if the gland nut has become loose. To cure a similar problem on modern taps, or to cure a tap which drips, refer to washer replacement
Tightening the tap gland nut
Undo the small screw holding the cross head in place (this may be hiding under a plastic cover in the top of the tap) and remove it.
Undo the top cover of the tap by unscrewing. This may be a metal type with a hexagonal base, in which case you should wrap some cloth around it before undoing with a spanner. The cloth will prevent it being scratched. Take care to prevent the tap itself from turning whilst doing this.
With the cover removed, tighten the gland nut at the base of the spindle with a spanner.
Hold the tap (wrapped in a rag) with a pipe wrench to prevent it turning.
Before reassembling, check that the nut is not so tight as to make it difficult to turn on the tap. This can be done by replacing the cross head temporarily without the fixing screw and testing the tap.
Repacking the tap gland
If this fails to cure the problem, turn off the water, remove the gland nut and repack the gland. Remove the old packing with a small screwdriver. Replace it with specially produced packing or, if you are unable to get hold of this, use string coated with petroleum jelly. Reassemble and test the function of the tap.