The alarm reportedly sounded for an extended period, causing disruption to nearby residents.
The council, which assumed management of the car park at the end of March 2025, stated it is reviewing procedures to improve response times and minimise future disturbances.
Efforts are also underway to repair the alarm system to prevent further incidents.
A spokesman for Epping Forest District Council said: “We would like to apologise to residents for the disruption the fire alarm at Cottis Yard car park caused on Easter Sunday.
“The alarm should not have been going off for as long as it did. We are looking into our procedures to ensure response times improve.
“Since taking over management of the car park at the end of March 2025, we have been working hard to fix the alarm system, reducing the number of instances and try to respond in a timely manner whenever it does go off.
“We apologise for the inconvenience and disturbance this caused over the Easter weekend and ask people to bear with us as we work out a solution.”