The batteries should be removed from the smoke detector prior to disposal.
Batteries should be disposed of at a battery recycling location; refer to Batteries in this A-Z list.
The older domestic ionization chamber type of smoke detectors (ICSDs) contain a very small quantity of radioactive material, and can be identified by their markings – they will have the word “radioactive” or a radiation symbol (trefoil) marked on them. These smoke detectors should be returned to the Manufacturing company who made the detectors.
The newer domestic photo electric smoke detectors do not contain radioactive material and can be disposed of in your domestic kerbside general waste red or green lidded bin once the battery has been removed from it.