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A bit out of date, but this interactive map of step free London is very good
All the London railway stations :
Beckenham Hill is on the ThamesLink network, and the whole station is step-free via side entrances onto both platforms. There are also boarding ramps available. It is not clear how you cross from one platform to the other. See pictures and further accessible transport detail from links below.
Underground lines : ThamesLink
AccessAble Access Guide :
Accessibility friendly : Whole station. Ramp to ticket office. It is not clear how you can get from one platform to the other, apart from 26 steps and a footbridge.
General description : See wiki
More comment : National Rail Guide & Maps