To answer your question, Bra sizes are very different here (sort of). Generally, you won't see smaller than a 34" band most often unless it is an A cup, so the cup size would be slightly smaller because the too large of a band compensates for it. ANy regular department store usually only carries up to a D cup, maybe a DD at most. This is because makers and stores often no longer carry the full range of sizes and just carry the most popular ones for profit margin. There are women who these sizes are all perfect for. So i guess the main difference is not as much the sizing but the range of sizes and what women do to compensate. Luckily I learned about british bras that i could get online, otherwise i certainly would be up the creek.
if you got a bathing suit that was meant for someone who was a 34DD or a 36D you would probably find that it works just fine. It might not have the snugness of the band that you want, but it would probably be fittable.
As far as dress sizes, I think you probably be about a 6 or maybe 8? do i have that conversion right , UK folks?