“Can high cholesterol cause higher BP?”

I know the two conditions have the same risk factors and that causes of high cholesterol are also responsible for high BP. But I'm wondering if it's possible that the first could be responsible for the second. I have high cholesterol, and am taking medication for it, but my BP has always been normal. For the last month or two though, it's been high. My GP did a lipid panel last year and my cholesterol had gone back up to over 200 (it had been around 165 on meds). Her recommendation was diet and exercise with no concern for the fact that it was this elevated while on medication (one reason why I'm getting a new GP and establishing with a cardiologist, just waiting for those appts now). If my new doctors up the dosage for the statin I'm on, or prescribe something else that lowers my cholesterol, is it possible my BP will normal out as well?

For the record, I am a little overweight, but not obese. Maybe 10-15lbs over what I "should" weigh. The cholesterol is genetic, I lost 40lbs and it went up, which is when I went on medication. I know diet and exercise can work, but it didn't for me, I just drew the short straw from both parents.