Richmond Railway Bridge
Richmond Railway Bridge in Richmond, Greater London, crosses the River Thames immediately upstream of Twickenham Bridge. It carries National Rail services operated by South Western Railway (SWR) on the Waterloo to Reading Line, and lies between Richmond and St Margarets stations. The bridge was amongst the first railway crossings of the Thames.

Richmond Railway Bridge in Richmond, Greater London, crosses the River Thames immediately upstream of Twickenham Bridge. It carries National Rail services operated by South Western Railway (SWR) on the Waterloo to Reading Line, and lies between Richmond and St Margarets stations. The bridge was amongst the first railway crossings of the Thames.
Check the official site before travelling; hours and prices can change.
More bridges

Tower Bridge
The bridge people mean when they say London Bridge. Walk the high-level walkway for the glass floor.

Millennium Bridge
Foot-only suspension bridge from St Paul's to Tate Modern — the only crossing aligned on St Paul's dome.

Hammersmith Bridge
Currently pedestrian-only, Victorian wrought-iron beauty — best photographed at golden hour.
Source: wiki-list