get down to your local Wilkinsons & buy "Grout Revive". Its made by Evo Stik. Its brilliant stuff & much, much, better than the grout pens that I really found quite hopeless. I used it on the grout in my bathroom & kitchen both of which were very grubby looking before. I've also used it on the grout on my stone kitchen floor tiles with good results too. Its around �3.15 for a tube. visit their site www.bostik.co.uk to know what you are looking for. I wouldn't suggest you use bleach
As cleversod says dettol mould and mildew remover, (green spray bottle). Once you have used this you won't use anything else.
I was only using it last night funnily, but wear old clothes and gloves if you can because it is quite harsh stuff with bleach and clorine in it so it can take the colour out of your clothes and sting your hands...been there!