Perhaps it's just semantics, but I dislike the implication from 'children's museums' that other museums aren't suitable for children.
I do enjoy many hands-on science places, such as Techiquest in Cardiff or @bristol, they are just like you describe - whole buildings full of great, fun, educational activities with loads to touch, poke around at and generally explore!
I think the difference is with some of the places like that I've been to is that they don't market themselves as being 'for children', although obviously children or families probably make up a large proportion of their visitors. However, they also attract many adults without children - they are also popular as company outings!
I just feel in this day and age, most museums are so welcoming to children, and geared up for all ages and types of visitors, that the idea of 'children's museums' seems a little odd. We've taken our 3 to museums since they were toddlers, and always found lots for them to do. Perhaps what you're describing would be more palatable to me under another name - I tend to go off things marketed as 'family-friendly' or 'children's'!
I think another poster probably was right when she said you might have to think more laterally - you might not find the exact sort of activity you were used to in the US, but there are still loads of great places to take children in the winter. It's a bit of a sweeping statement to say that outside of London the UK is full of soft play centres and nothing else! I'd have gone mad had that been the case, believe me!