Hi,
A lot of emergency equipment like that uses Lead Acid batteries with a connection to the power line for constant monitoring and charging if needed. It would detect the line power drop and turn the LEDs on for example, then start up the charging when the line returns. There are other battery types though that you may want to consider.
Since you are using multiple LEDs and not a single incandescent lamp like some do (or dual lamps) you can monitor the battery and switch off some of the LEDs to conserve power when the battery voltage starts to drop too low. That would keep at least some light going during the emergency power outage.
The 6v Lead Acid cells are popular, but i think the 12v ones are better.