Tower Bridge Magistrates' Court in Tooley Street is one of 157 courts which could close under proposals published by the Government this week.
Tower Bridge Magistrates' Court, a grade II listed building, has three courtrooms. Together with Camberwell Green Magistrates' Court it forms the current Lambeth & Southwark Local Justice Area.
The Ministry of Justice is proposing to merge the Croydon, Lambeth & Southwark and Sutton Local Justice Areas to form the South London Local Justice Area which would have courtrooms at Camberwell Green and Croydon.
A consultation document published by the Ministry of Justice says that two of the three courtrooms at Tower Bridge lack disabled access and secure access between the cells and the dock.
The building has a maintenance backlog of about £810,000 and costs about £268,000 a year to run.
"When public finances are under pressure, it is vital to eliminate waste and reduce costs," says courts minister Jonathan Djanogly.
"The Government is committed to supporting local justice, enabling justice to be done and seen to be done in our communities. Magistrates hear the majority of criminal cases and this voluntary contribution will continue to be strongly supported by the government as the bedrock of our justice system."
The minister added: "The Lord Chancellor and I are keen to hear the views of everyone with an interest in local justice arrangements. He will take all views into account before making any decision on which courts ought to be closed and when."
The Tooley Street court building is shared with the Metropolitan Police. The police station closed some years ago but officers from the flying squad are still based in the building.
The consultation is open until 15 September.