Very likely that although the power is getting to the lighter, the earth from the lighter is poor.
A quick wat to check (but be careful). push the lighter all the way in. Get a piece of wire about a metre long with bare ends on it. Put one end of the wire onto the shiny chrone ring which protrudes from the lighter That would be the chrome shiny ring which is visible and protrudes slightly from the dahboard even when the lighter is fully plugged.
The other end of the wire needs to go to any good earthing point in the car (somewhere like the bolts that hold the door hinges on).
If the lighter warms up and pops out then it is indeed the earth from the back of the lighter which is at fault (the black wire into the back of the lighter socket).
If however that does not work, and their is definately power to the lighter, then i suspect the whole unit is unserviceable. Halfords or any good motor factors will sell you a replacement lighter for less than £5 and fitting is a simple enough job.
Hope that helps.
Stephen H
November 2011