Well, I'm not a wubi expert and I don't even have Windows machine to try it myself but are you saying that initial boot configuration (used for first boot) doesn't contain any UUIDs? Looking at the error message provided by mikifin I think that's not the case:
Alert! /DEV/disk/by-ucid/1a16-46e4 does not exist
So it really tries to mount root by uuid. And it's the first boot so grub-mkconfig had no chance to run on Linux at this point.
Well, I'm not a wubi expert and I don't even have Windows machine to try it myself but are you saying that initial boot configuration (used for first boot) doesn't contain any UUIDs? Looking at the error message provided by mikifin I think that's not the case:
Alert! /DEV/disk/ by-ucid/ 1a16-46e4 does not exist
So it really tries to mount root by uuid. And it's the first boot so grub-mkconfig had no chance to run on Linux at this point.