Lying on your back does not restrict blood vessels that run to your baby. But the weight of your baby can compress the inferior vena cava which is a lrage blood vessel that carries de-oxygenated blood from your lower body (legs) back to your heart and then the lung to get oxygenated again.
If this vein does get constricted, you will feel quite uncomfortable, light-headed and maybe even out of breath. If this happens in your sleep, you usually just roll over without noticing.
The inferior vena cava runs along the right side of the spinal column which is one of the reasons why doctors recommend lying on your left side. The other reason is to avoid putting pressure on your liver which is on your right side.

I have been really trying to sleep on my left side and a body pillow really does do wonders. But I still sometimes wake up on my back or can't get to sleep in any other position. My mum slept on her back the entire time with both of her pregnancies and the babies were fien (if I may say so myself ). So I think the moral of the story is, sleeping on your left is ideal, but if you seelp on your left all the time, you will get pressure sores and sore hips and shoulders. Try to sleep like that as much as possible, but the main thing is to be able to sleep and get some rest. Sometimes I think we get too much information nowadays and end up driving ourselves insane. Don't worry too much, our grandmothers had healthy babies, too. And they probably slept on their backs, ate soft cheeses and lunch meat and generally just got on with their day.