Lewisham Council is working with police after unauthorised access was made to an IT storage portal.
The portal was being used by a council digital team for data analysis on a homeless project.
The council said they were not aware of inappropriate use but are making residents aware as a precaution.
They say 6,000 people and their financial details may have been affected.
Data like council tax, housing benefits, adult social care, education and planning could have been accessed.
Ian Thomas, Chief Executive of Lewisham Council, said: "Residents using our services are our highest priority. We sincerely regret this matter and are fully committed to doing everything we can to support those who may be affected."
If you are a resident you can contact 0800 953 3045 if you have any questions.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here