Mine was from John Lewis, it’s the baba bing Erin changing tote bag. I love it, has more space in it than it looks like it has, fits everything we need in it but is small enough to carry about with ease!
I've got this one... https://amzn.eu/d/d2kd1L5 I wanted one that i didn't have to dig for everything so it has a zip round the back to get things out from the bottom. It has side pockets inside big enough to fit a thermos and my nuby in one side. And all the pockets are on the side (5 in total and that includes a zippy one) It fits everything i need in it and even fits under my pram in the basket so i don't have to trek everywhere with it on.
Have you thought about just a normal backpack?