There's two aspect of "country" relative to somewhere like London. There's an estate in various towns, where there's plenty of actual public space, playing fields and grounds, walk into town, to shops, bus/train to larger towns. Plenty of open space.
Then there's the real country, where there's very little public space - nowhere to ride a bike other than narrow country roads, you can walk but only in restrictive footpaths over fields - some of which are sabotaged by farmers (I file 2 or 3 complaints with the right-of-way office each year as footpaths get blocked, barbed wire put over stiles, etc). We have an open forest area, but it's a 2 mile walk.
There are 4 children in our village at the "local" primary school, across the 7 years. My youngest's nearest friend is 6 miles away - again via 60mph roads. That means having to be driven to places. There is a school bus (which for americans reading is relatively rare in the UK -- you get one upto age 11 if you live more than 2 miles from the nearest school, or 3 miles for 11-16), but that doesn't help for after school clubs.
A toddler isn't going to be independent with travel, so driving them places is fine. In a few years though, you want them to be able to travel and meet friends, go to the shop etc, independently. That's easy enough in a city or in a town, not in the country.
That said, just having that access doesn't mean they will use it. My 13 year old's main social interaction is via minecraft sessions where they have a group call and yell at each other, doesn't matter if someone lives nearby (which one of the group does), or 30 miles away (which another does).
(It's worth highlighting that UK suburbia is very different to US suburbia)
> There are 4 children in our village at the "local" primary school
Four? How... What? How does any of this actually work (you clearly live there, so it obviously does?) That seems like you're living somewhere that's just like ... empty? How do any services/infrastructure/... How many old people live in this village?
Is this the demographic collapse people are going on about?
You're right. Personally, now that it's getting wet and cold, I'm getting kind of landlocked by mud. There's one tarmac road out in both directions, but only one of them leads to somewhere that somewhat resembles civilisation, or has pavement.