Most likely there is a broken cable within the cord from the base to the iron. You will need security bits, screwfix have them, to undo the base cover and a small screwdriver inserted into the iron top handle at cable entry to remove it for access to screws to remove main iron cover. You can then check leads for continuity. If broken try partmaster on web or Wykes, the official repairers on tefal site!
Fixit Lewis, September 2006