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A bit out of date, but this interactive map of step free London is very good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 :
Anerley is partially accessible, as there is step-free access onto both platforms via side gates. It is suggested that you could cross
platforms by exiting the station and crossing by the road overbridge which may be too steep a gradient. There are also train boarding ramps available on
request.
See pictures and further accessible transport detail from links below.
Overground lines : London Overground (East London line), ThamesLink
Accessibility friendly : Partially accessible.
General description : See wiki
More comment : Step-free access from station entrance to both platforms but not between platforms (TFL) as there is a 200 metre travel to cross platforms.
National Rail Map & Guide,