I haven't been able to find a picture but apparently they have curved necks.

I have seen a review carried out in 2010 which reviewed the conservation areas to identify which streets would best benefit from the alternative lamp posts. Each street within a CA was assessed on various criteria to give the street a score from 0 to 15. Presumably the streets will then be prioritised with the higher ranking ones getting the alternative posts and the lower ranking getting standard posts.

This is what the review said about the CAs in SE23:

Forest Hill: “More informal and organic than other conservation areas, reflecting its notable topography. Some strong streets but not characterised by the more ordered layouts as others are (such as Sydenham Thorpes, Telegraph Hill and others). It may therefore be appropriate to single out individual streets for special treatment.”

Perry Fields: “The streets defining the boundary of the conservation area, particularly Woolstone Road and Perry Rise, are part of a wider network of through routes and therefore not considered a priority for special treatment. However, the internal streets of Allenby Road and Garlies Road area enclosed streets fully contained within this conservation area and considered very suitable for inclusion.”

The review didn't identify which rankings would get the alternative design (it probably depends on how many Lewisham are willing to pay for). The highest ranking in the Forest Hill CA weren't particularly high:

score of 10:
part of Dartmouth Road

score of 9:
Benson Road
Havelock Walk
part of Wood Vale

score of 8:
part of Taymount Rise
part of Devonshire Road
Kings Garth

although Perry Fields CA fared a bit better:

score of 11:
Allenby Road

score of 10:
Garlies Road

I think it fair to assume that not all streets in a CA will get the alternative design. But as we don't know what the design looks like they may not be missing out on much!