It's not about comedy necessarily, it's about it being overall slightly light of touch, focused on domestic relationships with crime as the driving force behind the plot, and in the UK pretty much always rural. The ending can be sad but not depressing. It seems to be a British thing, really.
I was about halfway through writing one set on a baking show knock-off about leatherworking when someone published a book set in a knock-off of the Great British Bake-Off. Shame, I was enjoying writing it, but not enough to continue when it's already been done.
The US has some TV shows that are similar even if they don't seem it on the surface, but they're in cities because their rural is not the same as ours.