Playing out alone?

[Somethingsnappy]

At what age would you let your DC play outside, unsupervised? So, let's say, near the house, but out of site, on green spaces or in parks?

About 8

Just this year I've allowed my DD to the local park a five minute walk away with a bunch of friends.
She is 10.
The first couple of times I'll admit to popping down there to see what she was doing and if she was ok after an hour.

10ish

My second ds is 7 and a half and I let him start going round for abfew of his friends that lived nearby probably at the beginning of the year, he was either to stay and play in their street or come back round here though. Only in the last few weeks have I let him go to grassy areas and the park himself. Infact the first tkmebhe did it he was round at his friends and I didn't know about it. He loved it so I kept letting him, but only when he is with people.
With my eldest, he was a bit older, but he didn't have any friends that lived close enough that I felt comfortable for him to go alone. He was probably about 9.

It depends entirely on where you live. Is it safe in terms of roads? High / low crime area?

We live in a rural village. Crime rate is almost nil and the roads are quiet and there's a 20mph speed limit. I let my kids out to play (out of sight but within a couple hundred metres) by age 6-7.

We live in a large village (almost a town). Just some petty crime really in the area, nothing more. There is a fast and busy main road close by though, if the children were to stray too far away from the housing area. I know some people whose children, 5,6 and 7 play out alone. I can't work out if I'm jealous of their freedom, on behalf of my kids, or if I disapprove!

It's a balance between giving children the chance to have responsibility and manage risk for themselves vs actively putting them at risk.
I'd lay down the law and let them go out but trust that they won't go near the main road or else they'll not have the opportunity again. You can start off with short periods of time - 15 mins with a ball on the green etc.