You need to compare the caravan to your car. Your car insurance would not cover a breakdown, but it would theft, break-in, damage by a third party. If it broke down you would need a a specific breakdown cover.
Very few car breakdown covers also cover the van. Some will when it is attached and I think only one will openly say it covers the caravan when not attached to the car. This is the C&MC Mayday run by Greenflag.
In short, you will need a separate breakdown cover to cover any problems with the van. From memory, Lifesure offer a supplement o ntop of the caravan insurance to cover caravan breakdown. I was with Lifesure until this year when the premium went up a lot.
Colin