Could high blood pressure cause severe limb spasms?

Not typically. High blood pressure often has no symptoms at first which is why screening is so important. It is often a "silent" risk factor, meaning you don't know you have it if you don't look. Very high blood pressure can sometimes cause headaches or make you feel poorly. There are several causes of leg spasms, and if you get cramping in your legs with exertion (long walks) , definitely see your doctor!