The 34J's band is a lot longer than the 32K bra. While both bras have cups with similar depths, the 34J has wider cups, which may change the fit entirely.
What bra size am I?, How to Measure Your Bra Size
Millie Bra by Bravissimo, Ivory
Bra size chart – Bra fitting size converter
A Bra That Fits - Comparison of some popular UK 32H/US 32K/EU 70K bras. You can use this chart to figure out if you need narrower cups, more projected cups, taller cups
36G Bras and Lingerie, 36G Bra Size
I had a wonderful bra fitting - The Bra Boss of Kent
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34DD balcony bra - 32 products
What bra size am I?, How to Measure Your Bra Size
32HH - Bravissimo » Millie Bra (LN566)