I'm English but been away from there for almost 20 years now. I think most have "big" fridges now. Dont forget that those TV programmes are not recent - they were made years ago, even though they are still repeated on UK TV too.
I have a "big" fridge here - and a smaller one - keeps the wine cool!
I dont think there are many milk deliveries now, certainly in cities and larger towns - that is dying out, as people tend to do a "weekly" shop at the supermarket.