I heard a bit more today about the works at Honor Oak Park Station from London Overground's Project Manager.

In order to replace the stairs on the footbridge, new temporary stairs on scaffolding are to be constructed up to the road (both sides of the station). This will obviously entail removing a fair bit of vegetation.

Once the soil removal works by Southwark have been completed, it is expected that it will be possible to remove the old steel piling by platform 1 and regrade the side of the cutting into a gentle slope. This should dramatically improve the appearance of this side of the station but would obviously involve the loss of trees as soil levels are reduced. It will be interesting to hear Network Rail's story, but obviously their first priority has to be to provide a stable cutting.