Hi Andy,
Certainly sugar is one of the things that you need to cut right down on, but fat isn't. The foods that have the biggest effect in raising blood sugar are bread, cereals, pasta, rice and potatoes. They all contain high amounts of carbohydrates and it is carbohydrate that is converted into sugar in your blood. Fat has no carbs and therefore no effect whatsoever on your blood sugar. Also, contrary to popular belief, fat doesn't make you fat! But there's a whole "diet" industry out there making a fortune out of telling people that it does!
See if you can cut down on the starchy foods that I mentioned above and you should see an immediate reduction in your blood sugar. Have a good look round the forum, particularly in the low-carb section and you will pick up loads of tips on what is good for you to eat and what to avoid.
And just ask away if you have any questions.