Thanks for the advice, Exoventure!
The pencils I'm currently using are actually watercolour pencils, but I haven't tried using water with them yet. I think I'll try doing that to see how it turns out, maybe I can cover up the white spots with a little water and make it blend in with the rest so it's not too noticable. I have noticed something though, it's difficult to colour with certain colours (for me, red, black and grey) and I think it's because of my pencils themselves. I bought a new, different black from the same company and it's 10x better in terms of darkness and paper coverage. My birthday's coming up soonish, so I think I'll get myself a new set then.