Mark,
I am not familiar with your caravan, however you can run a seperate earth cable (single core) from one of the main earth points in the caravan (there will be several, look in handbook or online for a manual to find them). A good bet would be to run the new earth cables back to the battery charger as the 230v mains will be connected to the charger somehow and there should be an earth stud on it. Use a cable that is at least the same size as the conductors or larger. If you can get hold of a drum of 1mm or 1.5mm green/ yellow cable then use this as it will be big enough for wall lights (the conductor cables will probably be 0.75mm2 or 1mm)
If you are not confident working with electricity please get a qualified electrician to either do the work or at least check your work. The earth is there for a good reason so don't be tempted not to earth it!
David