Hi Clare
One reason your BP is low is because your veins and arteries are getting bigger to cope with the extra blood your body makes during pregnancy. By week 38 you can have as much as 70% more blood volume. So what is happening to you is that your blood vessels are getting bigger but your body has not made enough blood to fill them all. The only problem this will cause is that you may feel dizzy if you stand quickly. It will not harm your baby