This was already tagged correctly as motor_vehicle=private + private=residents

There is no *public* access for motor vehicles, but some motor vehicles not covered by other access tags are permitted to use it, specifically: A1 access permit holders and refuse collection vehicles.

It helps to read the traffic order in order to understand road restrictions, as these are usually published in The Gazette under the OpenStreetMap-compatible Open Government Licence.

The initial traffic order was The Newham (Prescribed Route) (No. 1) Experimental Traffic Order 2019, which I believe has now been made permanent.
https://www.thegazette.co.uk/notice/3347560

