Here is the official NHS info (it basically says don't worry what position you sleep in) www.nhs.uk/news/pregnancy-and-child/pregnant-women-should-avoid-sleeping-back-last-trimester/
and here is my summary from another thread:
Actually the studies that make this recommendation aren't clear cut.
No one involved in the most recent study actually had a stillbirth. All of the babies were born healthy regardless of what their mother's sleeping position had been in the weeks prior to giving birth. The conclusions did not definitively say that sleeping on your back in the third trimester raises the risk of stillbirth, it says that sleeping on your back does appear to have some impact on the babies' heart rate levels and from this they don't want to rule out the possibility that this could be a negative impact. However no long term negative impact was actually observed in the study.
An older study also making the claim about sleeping on your back possibly raising the risk got their data by asking a small number of women who had experienced a stillbirth what their sleeping position had been the nights before they gave birth. Now I can't tell you what my sleeping position was LAST NIGHT after an uneventful nights sleep and a boring morning. I'm relatively certain that I wouldn't reliably be able to tell a researcher what it was the night before an extremely traumatic event.
There is some evidence that sleeping on your back can cause you discomfort because of the weight of your uterus and baby squishing the blood supply. The point here is though that it causes discomfort, and naturally we tend to shift position if we are uncomfortable. Any midwife I have spoken to has told me that you would naturally move into another position long before it caused you or the baby harm. The caveat to this is if you have had an epidural and can't feel the discomfort - I think this scenario is specifically where some risks of being on your back have been identified.
The top and bottom of it is, if you are uncomfortable move into a position where you are more comfortable. I'm 32 weeks with DC2 and depending on where the baby is at the time sometimes that is on my right side, sometimes that is on my left side and sometimes that is in my back. I did the same with DC1. I think generally the advice is to try and fall asleep on your side 'just in case' but not to worry about it if you end up in your back during the night.