Hello Kevin,
I do not know what type of water system is fitted to your caravan, but it will be one of two types.
The most common system these days is a pressure switched system. This relies on the pump being able to raise the pressure in the pipe work to a value that is high enough to trip the pressure switch. The pressure switch is usually adjustable to allow for falling battery voltage. - Check the pipe work in the caravan where the pump plugs in. A few centimetres inside the caravan you should find a fitting with a knob on top. That is the pressure switch and its adjustment control. Check you caravan-operating instruction to learn how to adjust it.
The second and less common system these days, is a switched taps system. In each tap there is small micro-switch that turns the pump on when the tap is opened. This system is identified by a pair of wires to each tap.
If you have the switched tap system, and the pump runs when all the taps are shut, then you have either a faulty tap somewhere, or some poor wiring. In either case if it is a caravan under warranty or with a manufacturers guarantee, you dealer should be able to sort it out for you.