My 9 year old (year 5) started walking home by herself a couple of days a week this term. It's just under a mile, a few small roads to cross plus two larger ones with crossings. Large numbers of kids in her year have started walking on their own this year. A few walked/biked on their own last year but I personally wouldn't have let them if they were mine as I saw them crossing roads etc in unsafe ways.
She doesn't have a phone or a house key. If she is walking home then somebody is there waiting for her, so if she didn't turn up within half an hour of school finish time we would be out looking for her.
I think it does depend how sensible they are and how road-aware they are. If they have always been driven everywhere they are much less aware than if they bike or walk to school with you regularly. My daughter's always biked/walked about half the week so is used to crossing roads etc. As far as getting used to crossing roads is concerned, apart from just reminding her about things like not crossing by parked cars etc, I got her to tell me when it was safe to cross when we were walking together in order to gauge if she knew what she was doing. If anything she was overly cautious, which I took as a good sign.
Also the whole of year 4 and the end of year 3 she walked/biked of the last part of the journey in and our of school (not crossing a road, but going along a sort of driveway/pathway with garages on it). Now, her 7 year old sister has started at juniors they walk that bit together in the morning, and afternoon if I'm collecting them both.
I do think it is good to let them have some freedom, as long as you think they are sensible, and I do tell her if she abuses the trust put in her by doing anything stupid (eg not going straight to school/home) then she will lose that privilege and be accompanied everywhere again.
I suppose school can't actually say what parents and children can do outside of school but they can say children are not allowed to leave the school grounds unaccompanied without permission as they are in loco parentis during school time. Our infant school make it very clear you are supposed to bring children to the classroom, I'm sure they would not be impressed if children came on their own. And they are not allowed to leave without the relevant adult.