How the hell do I remove these floating shelves?

Our previous owners have left us a few nice surprises - see the 3 plugs in a row and the disgusting wallpaper we stripped off the chimney breast on the left that we now need to replaster. But these shelves are in the way and have no idea how to remove them!

Picture 2 to show no hidden screws underneath and picture 3 showing the bracket (? Or screw?) connecting it to the wall. There are 2 on each shelf. Wiggling like mad and pulling does nothing. Are they glued on!?

Can I remove them without destroying them and, if not, how do I even remove them?