I'd have expected the current to tail off too, but it doesn't.
The thread is here:
I didn't try removing the rather bright LEDs, which might have a bit to do with it. The LED does perform an additional purpose -- it's so bright that you can see your was to the loo in the dark without turning on the blinding 100W landing light, but I doubt whether that saves its overall cost in leccy.
As to whether burglars burgle more in power cuts, are there any statistics? I'd have thought that there was a good chance of finding a householder and fierce dog sitting by a candle behind drawn curtains.
Chris