The southbound carriagway of the bridge in Rocks Lane, Barnes, has been closed while a structural survey is carried out.
Richmond Council closed the carriageway and introduced temporary traffic signals after a number of bricks broke away from the structure and fell on to the railway lines below earlier today.
Network Rail, which is responsible for the bridge’s maintenance, informed the council about the fault this morning.
A spokesman said the bridge, built between 1885 and 1886, was structurally sound but further investigations needed to be carried out to identify the extent of repairs.
A council spokesman warned it may be necessary to close the bridge to all traffic once Network Rail has established the extent of the problem but said diversions would be put in place.
Trains are expected to keep running through the area.
Councillor David Trigg, Richmond Council cabinet member for traffic, transport and parking, said: “Network Rail is carrying out a full structural survey and we are waiting to hear the results of that before deciding whether both lanes on the bridge need to be closed.
“The bridge is owned by Network Rail and while we know this will cause disruption, we will work with them to ensure this is kept to a minimum.”
A Network Rail spokesman said: "Following the discovery of a minor structural defect on Rocks Lane road bridge, Network Rail has asked Richmond Council to impose a width restriction along one side of the carriageway.
"This will allow us to investigate further and to plan repair work, which we hope will be completed within the next six to eight weeks."
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