All the London railway stations :
Cannon Street is on the Circle and District lines which are partially accessible to wheelchair users.
The booking hall can be accessed from Ludgate hill without steps, or 11 steps from the Cnnon street entrance.
To access the westbound platforms, there is a lift, but
To access the eastbound platforms, there are 24 steps.
The station is also served by the Network rail network. The National Rail station is accessible to the whole station with lifts from street level down to platform levels. There are also boarding ramps available. See pictures and further accessible transport in London detail from links below.
Underground lines : Circle, District, National Rail
Accessibility friendly : Underground - Partially. National rail - yes.
More comment : National Rail Map & Guide.