The reporter suggests that they have been sent down a road that is set as Private Road, and that it is gated and pass only access. I have confirmed using GSV that it is gated, and would assume that Waze may have tried to send the reporter via this road to get over the M40.
I would guess the reporter was trying to get to Hall Barn Estate and this may be a staff only entrance?The main access looks like it is opposite the services on A355. As it is all Private roads Waze would use either route, with the one over the motorway being closest to the UR.
I would add an driving restriction to this segment, set to Prohibit All Vehicles, as you would do for an Access Only road. This should force entry via the A355.
You could also add a Place for Hall Barn Estate, linked to the Google place, and set an entry point near the A355