|I had the problem too - mine was caused by a defective thermal fuse under the 'boiler' in the iron. You will need a degree of mechanical/electrical skills to fix this but the parts only cost £1 from maplins|
If you are confident take the base unit apart (4 screws under neath - long phillips screwdriver) and very carefully position the top and bottoms so that you can plug in the unit and switch it on - check for the boiler getting warm by holding your hand some distance above it to feel the warmth rising - if it is cold there is a good possibility that one of the thermal fuses - 240C 250V 10A) is blown - ONLY DO THIS IF YOU ARE VERY COMFORTABLE WORKING WITH MAINS ELECTRICITY - NOT FOR AMATEURS. You will need to check the fuses with a meter and replace the defective one using some form of crimp connector. Replace the insulation over the fuse.