This path/track is called LILLEY UCR1, Status: UNMETALLED UNCLASS COUNTY ROAD
I'm struggling to get a description of this which I can understand in terms of mapping it BUT as the Chiltern Way hiking trail is directed along it on the OS Map (and I walked it today) I've given it foot access.

The road through the choker seems to be one way, southbound when I walked past BUT the nature of the signs is that they can be reversed, so I'm not sure how to map this

The supermarket is closed for redevelopment which will affect the whole area

I've added a branch of Puregym here which isn't open yet, but imminent

A path leaves next to the bottom of the steps, and goes through the woods then out again on the north side of the viaduct. You can eventually reach the service road. I imagine like on the other side, this is a permissive path?