There are two potential ownership problems when buying secondhand, stolen caravans and ones on HP.
If buying privately you need to be sure the seller has a good title. You can check the HP position with HPI and ownership with CRIS for a fee if you contact them with the serial number although neither are perfect.
Having done that you then need to make sure the seller has evidence of ownership and servicing records and if they cannot do this walk away as there are plenty more out there. Make sure there is a recent damp test report, or get a damp meter and check it your self.
Always make sure you see the seller at their home, not some storage area, nor have them bring it to you, as otherwise you cannot then guarantee they are who they say they are.
Get the seller to demonstrate that everything is working as things like heating and fridges are expensive to replace. If you know someone familiar with caravans it helps if they come with you.
Ask if you can have a caravan engineer check it over, even if you are not doing this. If they say no then be suspicious. You can get an engineer to check them, but it does cost, but in most cases it should be a wise precautions.
For a first time buyer a reputable dealer is a safer bet, you pay a bit more, but you should get a guarantee and everything should have been checked and be working. The choice is yours though.