Find a station or maybe an historical Pub or pot luck.

Accessible Train stations in London - Wallington

National Rail : ThamesLink

Accessibility friendly : Step-free access to Ticket Office and Platform 1 (to London) via main entrance. Step-free access to Platform 2 (to Sutton) via main entrance to Platform 2 (to the rear of Lidl car park off Beddington Gardens). Interchange between platforms is via subway with steps, which is not accessible friendly.

General description : See wiki

More comment : National Rail Map & Guide.