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A bit out of date, but this interactive map of step free London is very good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 :
Balham Junction is on the Northern Underground line and also National Rail. The Northern line is not accessible due to 30 - 32 stairs into the station booking hall. It does have escalators which avoid some of the stairs between the booking hall and platforms.
Balham undergound station
Balham undergound station stair access
The National Rail platforms 1 and 2 are served by a lift. See pictures and further accessible transport detail from links below.
National Rail : Southern
Underground lines : Northern line
Accessibility friendly : Northern - No. National Rail has partial accessibility. Step-free access to platforms 1and 2 via underground entrance from street via lift. Step-free interchange is possible between platforms 1 (to Croydon/Sutton/London Bridge) and 2 (to Victoria). When the underground is closed there is 1 step to gain entrance to the station.
Nearest step-free stations are Clapham Junction, Victoria, Streatham Common/Hill.
General description : See wiki
More comment : National Rail Map & Guide.