There will be separate heating elements for 12V operation, and 240V EHU (electical hook up).
It is possible that the 240V element has failed.
The 12V element being descibed as suitable for battery operation is misleading. You really need the alternator to be supplying the power and the battery is also connected to the alternator, as is normal.
To ensure that power is only taken when the alternator is charging the battery, a signal known as D+, is taken from the alternator field circuit, which only becomes live at 12V when the alternator is working, normally this is when the engine is running.
The D+ signal is used to operate a relay (fridge relay), which connects the fridge 12V element to usually, the starter battery.
On an x244 model Ducato it was common practice for the motorhome converter to fit two relays under the plastic hood at the centre rear of the engine compartment, the other relay would be the "split charge relay" which connects the habitation battery in parallel so that it can be recharged from the alternator. Both the split charge, and fridge relays should be connected to the starter battery via fuses, with the split sharge connection also having a fuse close to the habitation battery.
The under bonnet fuse and relay connections can suffer from corrosion, and it is not unknown for the connections to fail. Also the D+ connection to the relays may also be fused. If this fuse is faulty, there will be no 12V fridge operation, or recharging of the habitation battery while driving.
The fridge 12V element will draw about 13A, and can cause heating and hence further degredation of badly made connections. Look for discolouation of cables at connecting points.