I'd be checking your insurance policy documentation.
You should find your trailer is insured on a third party basis, however your issue is most likely the C&CC are viewing you as a showman or working for hire or Reward.
I had this with a race car on a trailer and its a very petty excuse to avoid responsibility in my experience, However Towergate Insurance (who the web tells me are now called Acer) used to specialise in these areas and were very good. I ended up insuring my commercial fleet with them for years.
The other option would be to contact the Showman's Guild and they should point you in the right direction.