Schools in my area (including the one where I work) all use shortest distance by road or maintained footpath in their admissions criteria, measured by the LA using their Geographic Information System. I understand they apply a layer of "safe route" information, though this isn't explicitly mentioned in the policies, which just say all routes need to be calculated by the LA.
In the past certain routes have been controversially excluded. Usually it is alleyways or routes through parks, but it's not something that they advertise - from what I've seen parents only find out when all of a sudden they don't get places.
A prospective parent at our Open Evening asked whether they might get a place. Nobody from their area has got in previously. They are out of borough but it looks like they're closer to the school than other people who regularly get places. They have to travel through some parkland - but it's a safe route used by commuters - I can't see any reason why it would be excluded from the "safe route" layer other than the fact that it leads out of borough (which shouldn't matter). I did tell the family to check this with the LA, and it has got me thinking as to whether they would have good grounds for appeal if they didn't get a place.