I tried on a similar dress in Cos - I really liked it but the way it was cut, there was no room for my breasts. And they’re not particularly big. I tried sizing up but got to the stage where I looked like a galleon in full sail, there was so much fabric billowing around me, and my breasts were still a bit squeezed. So you really do need to try Cos stuff on!
Try Seasalt if you have one nearby, they have plenty of cotton and linen frocks, including some plain linen ones.