We live very rurally, but I bet it isn't that different! We do a mixture of arguing about homework, catching up on housework, dog walks, various kids hobbies (swimming, horse riding, circus skills, rock climbing, musical theatre - we've been through a load). Maybe a trip to the cinema or a local site like a castle or the beach
My guess is we have better access to some activities (horse riding, outdoor swimming, beach) but worse access to museums, theatre and live music (although there is some).
We travel further to access things - no one thinks much of driving an hour each way to activities. But there's a culture of lift sharing with the other parents around (and we know every single family in the valley which makes this easier). The dc play out a lot, which I guess is less common in London - they go out on bikes or skateboards, play at the river in groups, make dens etc.
We don't have any access to takeaways (unless someone volunteers to pick something up when in town) and there's no last minute shopping so you need to be organised. Everyone has pantries and you have to be stocked up in case of getting snowed in in the winter.