Hi Matty,
Cutting carbs is certainly a pretty effective method of shifting body fat. The key, in my view, is in reducing insulin doses. As these reduce, your body will burn fat more effectively and have a reduced tendency to store it.
Be careful though. You will have to work hard at first to make sure your (reduced) insulin doses are still properly matched to your food intake. On the other hand, the very fact that your doses become smaller will help even out the rises and falls in your blood sugar level.
Hope that helps,
fergus