There are a number of products available for that purpose - Dettox do one and I'm sure Flash as well - they are usually called something like Mould and Mildew Remover. Spray on, leave for five minutes or so and then rinse off. Sometimes you need several applications to get rid of bad cases.
All of the above and Cilit Bang. It really does do what the adverts say. I gave in to my son who wanted to buy the thing that cleans pennies, I call it money laundering! BUT the stuff is fantastic. It got rid of the black stuff hidden in the corners of my bathroom, and other stuff too.
You must have a condensation problem (we did in our last flat) to avoid the mould growing back, invest in a de-humidifier....it does work, and you'll be amazed by the amount of excess moisture the machine sucks in !!!
It's not a condensation problem. The mould has built up in areas around the bath and seal where we just leave water to dry itself out afer we've showered. A product of our own laziness then, I guess. But this never happened in my parents house (and they never wiped all the excess water out of the shower area????)