At ASDA today, I found a super little cheese grater. The grater lies horizontally and fits over an oval shaped plastic bowl with a non-slip rubber ring underneath. The bowl also comes with a lid so you can store your grated cheese, carrot, etc.
I've had a go with it already and it works a treat. You don't have the same wrist strain that you get with those vertical tower types and you only need one hand.
I can't remember exactly how much it cost but it was around £2.50 - £3.00 and I can strongly recommend it!
Joanna