It is understood that the same incident has also affected Westminster City Council and Hammersmith and Fulham Council due to “joint arrangements”.
Hammersmith and Fulham Council said it “was able to successfully isolate and safeguard our network” and that there was currently “no evidence of H&F systems being compromised”.
However, the council was still investigating its systems and, as a precautionary measure, had temporarily suspended some public-facing applications, it added.
Westminster City Council said it was “continuing to respond to the cyber security incident identified on Monday 24 November”.
A spokesperson said: “We want to reassure residents that council services are running, although some disruption remains.
“Immediate steps were taken to contain the issue and protect our systems,” the spokesperson added.
Additional reporting by Adrian Zorzut, Local Democracy Reporting Service.