I use one of those net puffballs that are intended (I think) for scrubbing yourself in the shower. Get it wet and then squeeze it behind the tap and pull it from side to side. If necessary, use a squirt of Cif or some of Juliet's vinegar and bicarb. If the puffball is a bit elderly and has started to fall apart, so much the better - the strips of net are more effective once they are a bit loose. It is amazing how much dirt you can remove. It can be used to scrub the wash-basin and around the plughole too, and has a handy loop to hang it on a tap to drip-dry.