Hello Geoff,
You don't say if, or how much the other caravan was damaged (though I assume it was).
Without knowledge of the terms of the other caravanner's insurance policy, especially their limitation clauses, it is very difficult to give clear advice.
If the other caravanner had his caravan repaired or replaced by the insurance company, then you might be able to claim that the incident was covered by the caravanner's insurance policy, and thus a third party claim might have some legitimacy.
But I don't hold out a great deal of hope for you as you cannot make an insurance company pay out for what they are not liable. If the other caravan owners policy excludes sever weather, then the circumstances you describe I think might fall into that category.
If you could show that the other caravanner's had been negligent in some material way in the way their caravan was not secured or positioned, such that it was likely to cause damage to your property under severe weather conditions, then you might have a case against the owner. The burden of proof would be on you and I believe it would be difficult to obtain expert witness to support your prosecution.
With the benefit of hindsight, it may have been wise of you to insure your own property against such a loss, after all that is what insurance is for.