The problem may be caused by the dimmer having only 2 wires, so that it has to get its supply current through the lamps. Halogen lamps will let a small current though with minimal voltage drop, so the dimmer can store some energy like that each half-cycle to run its circuitry.
With LED lamps, there will be a big voltage drop when even a small current is taken, and the LEDs will light under those conditions, so the dimmer might not be powered correctly, and the LEDs will be lighting when they shouldn't.
It might be possible to separate out the supply to the dimmer from the load connection, making it a 3 wire device. You could then power it (via a fuse and a safety resistor) independently of the LEDs.
However, the devil is in the detail and that might not work at all well, it depends on the circuit. Also it is mains, so testing and diagnosing can be dangerous.