I had the same annoying problem with a new Homebase Monobloc Swan neck Kitchen tap - a residue of water continuing to flow after turning it off.
I contacted Hombase's suppliers who told me that it was capillary action,drawing the residue of water out and quite normal for this type of tap, but why in this age of technology should we have to put up with that ?
Fortunately, I was given a refund by Homebase when I was eventually able to take it back after paying a plumber £40.00 to fit a new and slightly different unit bought this time from B&Q. What do you know ? - same problem.
I noticed that my bathroom tap of similar design -only with a slightly lower swan neck - did not dribble and turned off immediately.
In both of my present taps, there is a small plastic aerator in a screw-on piece on the spout end of the tap. This gives a smoother flow with less splashing.
Comparing the two, the problem Kitchen tap had much larger holes in a different type of aerator and didn't stop the flow immediately.
As the two happened to be interchangeable, I spoke nicely to an assistant at the store who let me change my Kitchen tap aerator for a a similar one to that which was in my bathroom tap.
Problem solved. No more dribbles. Of course this may not work where a tap has no spout fixing for an aerator. It depends on the tap design.
Hope this helps.
Bob, November 2010