Honor Oak Road is not historically a main road. It is a narrow, twisty and hilly residential Rd. The P4 is designed for such roads.
Forcing its use as a main road is the underlying mistake that causes many other problems.
The road that historically connected Peckham to Sydenham perhaps back to the roman times is Wood Vale which is mostly wide, flat and straight.
But the residents on this road are even richer than those on Manor Mount and have long ago successfully repelled through traffic and bus routes.
Perhaps in Lewisham being a party member is more important than wealth, for having the influence to get traffic directed away from your own street.