Insurance Gap

I'm in the process of renewing my insurance cover on my caravan. I note that neither the CCC or CMC policies cover third party damage whilst the caravan is being towed.  I've checked with my car insurer who confirms that I have cover from them whilst the caravan is attached to my car.

The "attached" bit bothered me so I asked what would be the situation if the caravan became detached whilst I was towing and caused damage to a third party. Their view is that the moment the caravan became detached then their liability will cease.

Does that mean my unattached but still moving caravan is uninsured or does liability then revert to my caravan's insurer?