Help with bra sizes please

[SecretPineapple]

I've been wearing perfect fitting 38E Body bras from M&S for a few years. Recently I've put on weight and they no longer fit in the band. The cup size fits perfectly still, it's just the band. I've taken to using those bra extender hooks in all my bras. Even with these, my bras are no longer comfortable around the band.
The thing is, if I pull a measuring tape firmly around under the bust, it measures 38inches. You can see why I'm confused! I need a bigger band size because i can't do it up without the extender, but need the same cup size so what size do I go for?
(44inches over bust measurement if helpful)

If 38E is a good fit in the cup but you need a bigger band, try 40DD.

Oh so I can change the cup size but it'll actually still fit? Ok I will try that. Thank you for your help.

40DD has the same cup volume as 38E and it is a sister size. If you go up in the back you go down in the cup to get the same amount of boob coverage