HelloYvonne,
It is my view that provided the caravan you have used falls within the MPTLM specified by the vehicle manufacturer, then the warranty should stand.
If the manufacturer specifies a maximum towing limit (Which yours does) then it is unreasonable to claim that towing any thing up to that limit infringes warranty.
More importantly, as the manufacturer specifies a towing limit, and they make provision for the fitting of a tow-bar, and they approve certain makes/design of tow-bar, then clearly the manufacture is by default assuming the car may be used for towing. (If the manufacture did not wish it to be used for towing they would not set a trailer MPTLM, so the fact that one exists endorses the activity)
These facts are undisputable and set out as part of the specification for the vehicle. It establishes the purpose for which the car can be used.
Unless the seller has specifically excluded these applications, and can support their exclusion with reasonable written reasons as part of the contract of sale, it is implicit that the manufacturers specifications stands and represents the vehicle you purchase.
The seller cannot reasonably claim later that the vehicle is not suitable for towing up to its stated limit as this is a clear breach of the trades descriptions act and would also mean that the seller admits to selling a product that is not fit for purpose. Or as faulty at time of sale, both of which are breaches of the sale of goods act.
So the car is designed to accept trailer towing up to the manufacture stated limit. Thus of the gearbox fails and it is then claimed by the seller it is directly or indirectly due to towing, then the failure means the product is not fit for purpose, and that is subject to warranty.
If you have any difficulty in having the necessary repairs carried out by your supplier under warranty, contact a solicitor who will advise you of the best course of action.