Hello Floot
Sounds like exciting things are happening! I'm 35+4 and saw my MW yesterday. She said (and I've just checked on my notes) that they would want me to ring when I'm getting one contraction every 5 minutes, lasting 60 seconds.
However, as I'm in the sticks, if I was in your position, I'd have to take myself up to the nearest main hospital, instead of the local MLU, as it's before 37 weeks.
That said, baby should be pretty much fine at this point!
I've had BH since 20 weeks - to me they feel like my uterus going hard, not usually painful (but now that the baby's big, I can feel pressure on my cervix). They're not that comfortable, and I've heard other people say they are better if you walk, but I've found it more uncomfortable to walk through them. They seem to originate from the top, whereas I'm told proper contractions start from lower down.
If in doubt, ring your midwife.
Good luck with everything!