Not sure on stats, but my dd was breech at 37 weeks and turned several times cephalic and then back again between then and 42 weeks. Literally every time I was checked she'd turned the opposite way to the last time.
Of course she had to decide to be breech when I went in for a check at 42 weeks and having been told that there was no-one in my trust experienced enough to do a breech delivery or ECV. I was told I was looking at a CS the next day. Fortunately, they had overlooked one particular consultant, who happened to be on the ward and was very experienced in ECV. Having initially been very anti, after the consultant had talked it all through with me I opted for ECV over CS (for lots of reasons) and they did it there and then.
It was successful, she turned on the first try, no problems at all. Iirc, I was monitored for an hour before and afterwards to make sure she wasn't in distress. I was scanned using a mobile scanner to check placental position etc, literally a couple of seconds before he turned her and then again afterwards. I spent a couple of hours being generally monitored at the hospital before going home and sitting bolt upright all night to stop her from turning again! I was then induced the next day and had a very speedy delivery with no complications.
The consultant said they would only try twice and wouldn't try for longer than either 30 or 60 seconds at a time (I can't remember which sorry). He was insistent that both mine and the baby's health were the most important thing and they wouldn't pursue the ECV if there was even a hint of a problem, hence all the scans, checks and monitoring.
32 weeks is very early days, but I totally understand how you are feeling, because I felt the same when they told me dd was the same. I had planned a home water birth and we had everything set up and good to go. I am also phobic about hospitals and surgery in particular, so the idea of a CS terrified me. Dd was my last baby and I desperately wanted the kind of birth I had planned, but in the end, all that mattered was that I had my beautiful baby in my arms safe and sound. Okay, she was delivered in hospital (in a side room as I didn't make it to delivery) rather than at home, but it really didn't seem important once she was here, iyswim.