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A bit out of date, but this interactive map of step free London is very good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 :
Battersea Park is on ThamesLink national rail network, and it is not an accessible public transport station for wheelchair accessibility due to the steps to platforms. See pictures and further accessible transport detail from links and detail below.
National Rail : ThamesLink
AccessAble Access Guide :
Accessibility friendly : There is no step-free access to platforms from street , although step-free interchange is possible between platforms 2 (trains to Victoria from the South London Line) and 3 (to Clapham Junction). Boarding ramps are not available. This is not an accessible station. Nearest step-free station is London Victoria.
General description : See wiki
More comment : National Rail Map & Guide.