Oh boy…it’s hard to say because there is no consistency in bra sizing. For some brands, it’s a 34E, for others, it’s a 34F (which is so not helpful, I know). Instead, I’d recommend resizing yourself as you’ll get a closer fit to your UK bra size using another fit method.
Measure your underbust, measure your overbust, and then a add a cup size for each inch of differences between them (1” = A cup, 2” = B cup, 3” = C cup, etc.). You’ll also want to be willing to try sister sizes (for example, if your size comes up 34E, then the sister size would be 36D) because seriously, there is no consistency here and it’s a whole heap of trial and error.
Sorry I can’t be more helpful.