It has taken a long time to get an answer, but this is why TfL changed their mind:
Please be advised that it was our original intention to provide a pedestrian refuge in Waldram Place to assist pedestrians crossing. However, further investigations revealed that due to their wide turning circles, large vehicles would not be able to turn into and out of Waldram Place if a pedestrian island were provided. Waldram Place is part of a diversionary route that is used by those vehicles which are unable to pass under the low railway bridge on the A205 Waldram Crescent. It is therefore [potentially] used by many high vehicles.
To address this issue, consideration was given to banning vehicles over a certain size from turning into and out of Waldram Crescent, and instead using Perry Vale (B227). Signs could be erected at - and in advance of - Perry Vale to re-direct drivers of high or large vehicles there. This would be the last opportunity they would have to turn off the A205 to avoid the low bridge just west of Waldram Place. However, from Perry Vale this bridge is not visible, and it is therefore likely that any instructions on these signs would not be followed. If drivers miss Perry Vale and are no longer able to use Waldram Crescent it would cause delays and difficulties on the network.
I had rather expected that it had something to do with vehicle tracking, but had not suspected that it would be from the Catford direction.
We did suggest in 2010 that they move the pedestrian crossing further up Waldram Place to beyond the entrance for the MOT station, but this was rejected out of hand.