SE21, SE22, SE23, and SE26 have been affected by the incident, which began on the evening of January 5.
The water main burst on Lordship Lane.
Thames Water has apologised to customers and confirmed that teams are working to restore service.
A spokesman for Thames Water said: “Sorry if your tap water isn’t running as normal at the moment.
“We’re aware of a burst water main on Lordship Lane.
“Our specialist teams are in the area and working on a plan to restore your water supply.”
Thames Water has offered advice to residents who may need extra assistance.
A spokesman said: “If you or someone you know needs a little extra support, our free Priority Services Register can help us to understand your situation so we can take it into account as best we can.”
The company said the repairs are complex and are taking longer than usual.
In its latest update at 7.20am on January 6, Thames Water said: “Our specialist team are on their way to investigate and resolve the issue.
“Due to the complexity of the repair it is taking longer than usual to restore your water supply.
“Customers in the postcodes listed below may experience low water pressure or a temporary loss of supply while we work to resolve the issue.”
Further updates are being provided on the Thames Water website.
Residents wishing to register for Thames Water’s Priority Services Register can do so via the company’s website.
