Hi Andrea, I am 35+6 and I can sleep on either left or right side!
I think when i was about 28weeks I would wake up on my back a lot, and it would worry me as I know it's not really good.
In recent weeks I have had big problems sleeping at all, mostly I was getting 2hours on, 2hours off, etc. In all honesty I didn't think those pillows that red mentioned would be much cop, but my hubby bought me one over the weekend and... my god... what a difference! I slept well the first night I used it and then last night I slept from 9:30pm until 5:30am this morning, and even when I do wake throughout the night it is easier to get back to sleep because it is easier to get comfortable! It was �25 from Argos, although I am sure if you look around you will probably find one cheaper elsewhere.
As red says, sleeping on your left side is best as it gives best circulation (and can help with swollen ankles, etc, if that is a problem), however any amount of sleep on either side is a start! LOL