Teddington has a footbridge which can be used by the general public to cross the line as well as to access the platforms.
There's dividing fence on the footbridge which makes me wonder if in the days of manned ticket barriers the outer side of the stairs and span were for non-railway pedestrians, and the inner side of the stairs and span were for passengers, with the ticket barrier on each side being placed by the fence at the foot of the stairs. This would make sense, as Teddington is a junction station for the Shepperton branch, and passengers going there from Twickenham, etc, have to cross the line to change trains.
I have a feeling that the footbridge at both Mortlake and Strawberry Hill serves both non-railway pedestrians and passengers; there's a level crossing at both stations and the footbridge is useful for passengers and pedestrians alike when the barriers are down, which they can be for quite some at Mortlake.
I also think that the subway at both Kew Gardens and Norbiton is outside of the ticket barriers so it can be used by non-railway pedestrians. Kew Gardens also has a footbridge that can be used by non-railway pedestrians, the steps are outside the station, thereby avoiding a 10-minute walk in either direction to the next crossing point. The subway at Norbiton cuts off a couple of hundred yards for people wishing to cross the railway to get the hospital.