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East Finchley is on the Northern line underground, and is NOT accessible to wheelchair users due to 30 stairs between street level and platforms. See pictures and further accessible transport in London detail from links below. There does appear to be a raised platform at parts of the train, allowing easy step-free movement on and off of the train, and you can easily cross between the southern and northern platforms.
Underground lines : Northern
Accessibility friendly : East Finchley is not accessible to wheelchair users due to 30 stairs between the platform and street level.
More comment : Inclusive Britain Station Guide