How does UK bra sizing work?

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Bought myself a proper bra for the first time in years and clearly ive put more weight on than i realised

Bought a 32DD and both the band is too tight and im spilling out the cups.

Measured myself and i think band is 34 and bust is 38-39

Online calculator says i should get a 34DD but surely if the cup is the same size im still gonna have the spillung out problem?