Definitely try the boob or bust calculator. I used that and bought bras in that size to see.
If a tape measure fits around you at 31 inches, then a 32 back bra would fit! Possibly even be too big. M&S are terrible at measuring! Even though they have supposedly changed their methods. Boux Avenue are better, however even they added inches to my underbust – I think the fitter was inexperienced and panicked a bit!
Your best bet would be bravissimo if you can get to one xxx