Unfortunately, this created an issue rather than fixing it. Adding motor_vehicle=designated means that the road is intended for use by ALL motor vehicles. Signage at the entrance is no entry (for all vehicles) except local buses.

TfL and bus company tow trucks and Newham street cleaning vehicles have explicit permission which is covered by access=private.

I have re-tagged the roads as access=private + bus=designated and removed the motor_vehicle=designated tags.
https://www.openstreetmap.org/changeset/152728183