I can not see that the police would get too involved unless there is some criminal element to what has happened.
I would ask the caravan site for the legal documentation which they claim confirms they have the legal ownership of the caravan, they are going to have to provide this at some point as there may be a legal dispute. You do have documentation of the sale between you and the owner of the van which I would make sure the site has copies of but see theirs and note the date of sale.
Make sure you deal with the correct people on the site, not just front desk office staff, contact the legal team of the site make sure they are aware of the original sale between you and the owner.
I would send the site and site legal team copies of your document of sale by recorded delivery.
All that has happened at the moment is your caravan is on a site claiming to own your caravan, you have documentation of proof of sale what do they have. The original owner terminated his legal ownership when he sold you the caravan so was not the owner of the van at the time the site is claiming he sold it to them.
You need to see and obtain a copy of their sale agreement first...Dates are important.
And yes legal advice from someone specialising in caravan sales not just any Solicitor, they do specialise.