That does suggest that you are heading the right way with the 34 though - I would do another session but this time start with say a 34G. Put it on and scoop very thoroughly. Now, once the fit is right all that back fat will stay in ( you've seen how it works on the current bra!)
Depending on the bra, if the cup is too small scooping either just won't work (and it'll stay at the armpits/back) or it will come away from the back and escape out the front. Depends on how low the bra is. So, if after you try to scoop you either have armpit bulges, backfat or quadboob, go up another cup.
Out of interest - what brand were you trying in Debenhams? Their own brand, Gorgeous, is a bit of an unpredictable mare size wise.