The most common fault on headlight removal is the hexagonal nut head or socket tool rounds off, but you say this is not the case here and you suspect the clamping rod is broken. This would be rare. 
But if it is the case, it means the lamp is no longer clamped and you should be able to remove it by pulling it forward - use a pair of marigolds for a better grip! [
] Or you could try gentle levering with a plastic trim pry bar around the rim to loosen it - use masking tape to prevent paint damage.
Removing the front section of the plastic wheel arch liner, you may be able to reach into the back of the headlight and loosen it from there.
My bet would be it is a rounded hex on the bar, so try a slightly smaller socket on the end of a 1/4" extension and see if you can tap it on for a tight fit.
Regards,
[font="comic sans ms,sans-serif"]Clive[/font]
But if it is the case, it means the lamp is no longer clamped and you should be able to remove it by pulling it forward - use a pair of marigolds for a better grip! [
Removing the front section of the plastic wheel arch liner, you may be able to reach into the back of the headlight and loosen it from there.
My bet would be it is a rounded hex on the bar, so try a slightly smaller socket on the end of a 1/4" extension and see if you can tap it on for a tight fit.
Regards,
[font="comic sans ms,sans-serif"]Clive[/font]