Hello Freckles, welcome to the information blackhole that is placenta praevia and the NHS!
When you say it's within 2cm of the os, is it covering the os? And is it anterior or posterior?
At 20 weeks, I had internal scan showed my placenta was 8mm (0.8cm) away from os, but wasn't covering. My understanding is that if it doesn't cover os, but is nearby, it is a grade 1 and the least threatening, as a ridiculously high proportion (95% plus) of these move away by full-term.
If it is anterior, it is even more likely to move up out of the way, as the uterus expands more along the front than the back, so the bit between the os and the placenta stretches in a sense.
Posterior placentas still move, but not to the same extent.
It's good that they are rescanning you - I found out a couple of weeks ago that apparently my Trust don't rescan unless placenta is completely covering the os at 20 weeks. This was after being told that I would be rescanned and that I couldn't fly by two separate midwives.
I now have a niggling 'what if mine hasn't moved' worry but won't find out until delivery day if there's a problem or not!
Really hope you don't get any more bleeding (did they confirm it was from the low placenta?) and that you get the peace of mind you need. Most placentas move out of the way - and at least you get a chance to see you LO again before delivery day.