Jules ... how does that unit switch? It looks for all the world like a straight forward power supply I have for the LEDs in the kitchen.
It doesn't, it just supplies 13.8V at the output as long as the mains is on. No mains, no output.
In the caravan it is just in parallel with the battery and, as such, maintains it at float voltage. Loads connected to the battery just draw power from the power supply (unless they exceed it's capacity I guess but nothing seems to do that).
When there is no mains power, the loads just take their power from the battery.
I know it is probably not the best for the battery but it works. Most caravans have a similar system (just the commercial ones are a lot more expensive).