The building houses Newington Library, a museum of Southwark's history and a one-stop shop for residents to access council services.
Leader of the council Peter John said: “Whilst our first concern is for the safety of residents and our staff, we are also worried about possible damage to the museum's collection.
“It does not appear at this time that surrounding buildings or any residential properties have been affected, but we will continue to monitor the situation very closely and continue to assist the emergency services where we can.”
