The children played in the road (hardly any cars) and in a parkNow I see children in nurseries behind substantial railings
The family may or may not know the neighbours at all
There's a separate issue which reveals itself in what you say but which wasn't specifically addressed.
A big reason for less community cohesion nowadays is that no longer are large numbers of parents staying at home and interacting in the community while looking after their kids. Instead, the majority are going to work and putting their kids in nurseries instead.
I live in Lincolnshire where many of the villages used to have thriving communities and shops, yet are now commuter villages and everyone has to drive to town to buy things instead.
The reason? There aren't hundreds of (mostly) mothers milling around acting as the glue for the village communities. Instead, they're all out at work and the kids are in the nurseries in town.
This isn't a particularly politically correct point to make, however, since obviously mothers should be free to work if they wish, but the movement of millions of mothers from daily community life into the workforce has had a serious impact on modern British society.