You've not updated so it's hard to say if tabu or yanbu.
If it's no more than 10 minutes away, with no busy roads, I think YABU. Most local children are allowed to the corner shop/tesco express round here by 8 years old. When I was a child, my mother was overprotective and I was usually the last of my peers to do things but at 9 I was allow to the corner shop, 5 mins away, across a road, and visiting friends would accompany. No one would have thought to ask visiting kids parents if it was allowed. My town hasn't changed that much and it was no more safer then than now.
I was under strict instructions, straight there and back and if I took too long choosing sweets I'd often find my distraught mother charging up the hill to look for me.
Two years later, in Yr 6, I'd be travelling on buses alone to meet my Mum in town after school, largely to prepare me for Yr 7, when most kids have to make their own way to school or hang out independently with friends after school/meet them in town at weekends. Prior to that I'd do the 15 min walk home from school alone, along busy roads, past pubs etc...I was only 18 month older than your son is now.
The kids at local primary schools all seem to do the same these days, and many are younger than I was.
If your son can't go to the nearest shops to buy sweets in Yr 4 or 5 (if he's 9 now), when are you going to start letting him go?
Providing it's a relatively safe, local, place, that is and we aren't going be drip fed a story about a 30 minute walk along rural lanes in the middle of nowhere or across a drug addict riddled estate where knife crime is rife!