Hi,
The lack of power is then why the lighter wasn't popped out.
if you have a voltage tester you can check to see if both sides of the fuse (when fitted) have power or whether there is power to one side of the fuse socket with the fuse removed.
View attachment 16153
The Cigarette lighter fuse goes to the permanent live so power should be always on. If there is power on the fuse and the fuse is OK then the problem must be between that and the socket.
The curved plastic piece holding the socket just clips in place, but to remove it you must first remove the handbrake grip and plastic cover. The handbrake grip has a small metal clip holding it in place which is accessible from underneath just by the release button through a small hole. Once the clip is pushed in, the grip slides off past the button. It can be stiff but must be released first! Once the grip is removed, the plastic cover can be slid off the same way.
regards
Andrew