All the London railway stations :
East Dulwich is on ThamesLink with some accessible access to platform 1 only via a steep ramp. See pictures and further accessible transport in London detail from links below.
National Rail : ThamesLink
Accessibility friendly : Step free access via steep ramp to platform 1 (to London Bridge) only. Steps to platform 2 (to Tulse Hill). Step-free access to Ticket Office from street. Nearest step-free station is London Bridge, West Norwood or Mitcham Junction.
General description : See wiki
More comment : National Rail Map & Guide.