The best blood pressure and lipid profile/cholesterol results I get are when I'm following my 30g of carb per day Atkins-style diet to the letter (it's a sticky thread in the Low carb section if you want to look at it). On this diet, my blood glucose levels are normally within the non-diabetic range. I don't consider it a high-fat diet, though obviously it can be, depending what you eat. I eat good, unprocessed fats and I don't go for them deliberately - I just don't avoid them. If my diabetic specialist GP was to see what I do eat (mayonnaise; 2-egg omelette cooked in butter almost every morning; leave fat on meat) it would be she who had the heart-attack!
Some people get an initial rise in total cholesterol when they first go low carb/high fat, but that seems to be caused by the fat-burning phenomenon (ketosis), as the stored fat is used for fuel. Usually everything settles down. You should not just look at total cholesterol, but at a full lipid profile - HDL, LDL, triglycerides and the Total/HDL ratio. Ask for a copy of your results and get your GP to explain them. If the GP can't/won't, come back here and ask!
The problem is, if your cholesterol drops the GP will say it was the statins that did it! I won't take them, but my lipids are still fine. Many people get on well with statins; I didn't, even on a very low dose, so I don't take them any more.
Hope this helps. Let us know how you get on.
Viv 8)