you need the kind of thick bleach that is designed for putting in loos, a throwaway paintbrush (or more than one, the bleach eats the bristles) old clothes and disposable rubber gloves, eye protection (old sunglasses will do). Ventilate the room well. paint the bleach on over the black stuff, leave for 24 hours, rinse off well with plain water. This always works for me but do be careful, the bleach is vicious. Dont get it on the chromework, especially if you have fancy brass or gold plated stuff.