[embee]

Agree, this is bloxxox.

The insurance is unlikely to cover the repair to the fence, but damage caused to a third party by a panel blowing out is exactly what should be covered.

Whether you're insured or not doesn't affect your liability.

Whether the owner of the fence is insured or not is frankly their concern, the party suffering the damage simply sues the owner of the fence for the damage and it's up to them how they pay for it. Your (the aggrieved)Household insurance might well have legal assistance to help you deal with this.
Small Claim at the County Court would probably be an option providing there's a reasonable chance of the fence owner having some money to get hold of.