Well obviously you have got to accommodate your IBS so you are obviously the expert on that, not me - but since it is proven that eating fat does not increase serum cholesterol and therefore has little if any effect on heart disease/hardening of the arteries, the fact that the NHS clings so tenaciously to recommending low fat diets to all and sundry completely baffles me!
The thing - almost the only thing - that we eat which increases our BG is carbohydrates. End of story! It doesn't matter where they come from really - sugar is merely another carb but because it is near enough 100% carb, it's obviously the first thing to try and cut down on wherever we can - and sugar in teas and coffees is obviously the first port of call. The next thing to look at reducing is 'starchy' carb - so that's anything containing wheat flour for starters (bread, pastry, thickeners for sauces, cake, biscuits) and pasta. Then we have potatoes and also rice. plus root veg - cos parsnips are also ridiculously high carb, and then others such as carrots and swede have a bit less. Then fruit - some of that is ridiculously high in fructose, especially eg oranges - the fibre in them hardly slows the rate of absorption of their carb down at all - hence why 'pure' orange juice is such a popular and effective worldwide hypo treatment choice for insulin users!
Dietary fat is very useful to diabetics, especially those who have a decent supply of their own insulin - because fat eaten with carb (so butter on the bread, cheese on the pasta, etc) slows down the rate at which the carb is absorbed by the body thus giving the 'slowed down' ability of the body to produce the insulin and deal properly with the carbs, more time to do it in.
You may well not have to cut everything out by gradually testing foods, testing BG before and after eating, to find out how much of what, your innards can cope with - see
http://loraldiabetes.blogspot.co.uk/2006/10/test-review-adjust.html for how to go about this methodically.
Good luck with it - you'll get there!