The study looked into 291 pregnancies that ended in stillbirth and 735 women who had a live birth.
Researchers say the position which women fall asleep in is most important - and they should not worry if they are on their back when they wake up.
About one in 225 pregnancies in the UK ends in stillbirth and the study authors estimate that about 130 babies' lives a year could be saved if women went to sleep on their side.
The MiNESS study, published in the British Journal of Obstetrics and Gynaecology (BJOG) is the biggest of its kind, and confirms findings from smaller studies in New Zealand and Australia.
Prof Alexander Heazell, clinical director at the Tommy's Stillbirth Research Centre at St Mary's Hospital in Manchester, who led the research, advises women in their third trimester to sleep on their side for any episode of sleep, including daytime naps.
"What I don't want is for women to wake up flat on their back and think 'oh my goodness I've done something awful to my baby'.
"The question that we asked was very specifically what position people went to sleep in and that's important as you spend longer in that position than you do in any other.
"And also you can't do anything about the position that you wake up in but you can do something about the position you go to sleep."
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