SK53
A track without an access or designation tags in England and Wales should ALWAYS be assumed to not allow public access. It may be that Mapbox need to take that into consideration when creating maps for these jurisdictions. Note that the contrary applies in Scotland. 

For reference the Ordnance Survey maps show this track and makes no distinction from other roads: http://www.cucaera.co.uk/grp/?refs=SU894845&map=ordnance_current&vcs=true&graticule=true&nsgrids=false&zoom=15&lat=51.55384717298128&lon=-0.7170724868774414. So if someone is complaining about people using the track then ask if they have also complained to the OS. 