I'm sorry to read of your misfortune.
I Will relate an experience that a friend of ours had which might explain a claim solution for you.
Our friend had to stop at a red traffic light on a dual carriage way. He was in the off side lane with two cars in front of him, and a coach in the near side lane.
The lights changed and the cars pulled away more quickly than the coach, and as our friend was just moving ahead of the coach but still within the junction, another car jumped the red light drove into the junction from the offside 'T-boning' our friend pushing him into the front offside corner of the coach. The coach pushed him several meters and into a set of bollards. Fortunately no one was hurt. But because a public transport vehicle was involved the police were called, measurements taken and evidence gathered.
The police were totally in agreement that the driver that jumped the lights was to blame and duly prosecuted. But the insurance was a different matter.
THe highway authority claimed of our friend for the damage to the bollards and sundry costs, because it was our friends car that had collided with them. The Bus company claimed of our friends again because it was his car that collided with the bus.
It was down to our friends insurer to counter claim against the driver of the red light car.
So the president is that these days you can only claim against the party that directly injures or causes your loss - in your case your neighbours caravan. It seems you probably don't have a direct claim against to owner of the first caravan that went on fire.
As Parksy correctly points out, you may have a claim against the site if they have contravened their own site rules such as caravan spacing, or fire spread prevention measures, or those imposed or recommended as best practice by the the licensing authorities.
Just as an aside note, There is nothing stopping you taking out insurance on a caravan even if you don't have all the documents.