Here in Germany most kids walk to school with their peers and without their parents. It's almost 2km away and some as young as 6 go alone or with their friends.
The fact that I walk with mine (6&9) to school in the morning makes me a helicopter mum here - but it's because they want me to. Sometimes my 9-year-old walks back alone from school, slowly gaining independence. They will both scoot to the local shop close to school on their own sometimes, and I'm good with it, she often meets her friends on the way or in the shop, also buying sweets without a parent.
I also leave them for an hour or two sometimes to go to the supermarket and they're fine. She's a great and responsible big sister, and it's the norm here.
The UK is similar to the US, where parents drive their kids everywhere. There is something to be said about giving them independence from a young age, but in small increments and only when they're ready - which they usually are before the parents are.