The only thing I've found which helps bring back the white grout is Dettol "Mould & Mildew Remover". It's not cheap and has a really strong smell, but you spray, leave it on for about 5 minutes and it actually works - at least it does for me! Hope this helps!
HG mould spray, amazing stuff. I moved into a house where the grout was black. I tried Astonish mould spray, when that didnt work the Dettol one, when that didnt work I spent 3 days painting the grout with bleach & dissolving numerous paint brush hairs while I did it. It helped but didnt really work. My mum bought me a bottle of the HG stuff & it sorted it in an hour. I cannot recommend it highly enough.
Cillit Bang to an active foam bathroom cleaner (not the spray bottle version) which you spray on, leave and watch all the gunk trickle down the walls. Just rinse it off afterwards. It's brilliant on dirt, although I'm not sure about actual mould.