I have just sorted the same problem on my van. The power supply was working fine, everything 12 volt worked with mains connected, but the battery wasn't charging, and the 12 volt lights wouldn't work if the mains was not connected.
After spending several frustrating hours with a multimeter, i worked out that everything on the power supply side was working fine, including the output circuit for battery charging. That only left one thing - the cable that runs from the power supply to the battery. I put the caravan up un ramps and climbed underneath. I found the cable that goes to the battery and there was a connector in it. I pulled the connector apart and found the metal blades inside had corroded away. I bought and fitted a new connector, and filled it with silicon sealer so it is completely sealed against moisture ingress. Problem solved.
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