He sounds sensible
He really really doesn't. Did you read the part where op can only get the twins in and out the flat if dh or a neighbour is available to help? And otherwise she is stuck in the flat unable to leave? That is a crazy situation. Clearly they need a more suitable home, whether they can afford it in London or need to move elsewhere (not necessarily Wales).
There will be less work in Wales
They need to do sums, but he isn't working much in London as it is and living costs high. If their living costs are so much less in wales and op can work with family childcare, it may well be financially better off to move to wales despite him earning less there.
you’ll be putting the burden of childcare on others
Which some family members are very happy to provide, and don't see as a burden. Depends on what op's family think. I know grandparents who really want to provide free childcare for their grandkids.
he won’t be happy there
Op isn't happy in London for understandable reasons, especially when she physically can't leave the flat. It also in honesty doesn't sound good for the kids - bad schools, main road outside, not near green spaces, no outdoors space.
not to mention he will have to finance it
They need to decide together. Being the (current) wage earner doesn't mean he gets to make the decision.
You chose to have children where you are now so knew what you were getting into and went ahead anyway
I really disagree with this. Things change, priorities change. We live in London with young kids and we discuss together whether to stay or move away. Lots of parents move out of London as their kids grow up, despite being very happy there before kids, it's a well trodden path. They would have planned for one baby rather than twins which might have meant op's wages would be greater than childcare, and the presumably didn't expect her dh to have less work available, so they would have had greater income. With this they could have lived in a more suitable London home eg flat with lift near good schools and park, which could have made all the difference.
Your current living situation sounds dreadful and I think your dh is being selfish to not consider moving somewhere, although there may be better options than wales.