You do need to inform your insurers if towing any trailer.
Your car insurance will cover the caravan for third-party claims while on the public highway but not for damage to the caravan.
Many of us arrange insurance over the telephone. A verbal contract such as this is just as enforceable as a written contract, insurers often record calls anyway. Since you would have no record of giving this information, CliveV's advice to inform them in writing is sound.