Spoke to my insurers who said that there should be no problem accepting the cheque as the third party insurers have admitted liability and are therefore responsible for the full repair. They also said if additional work is discovered then a new quote would be required and the third party insurers may want to inspect before they approve. My insurers can get involved if there are any issues, but this is highly unlikely. The main issue after an accident is determining who's fault it is and this is where I would definitely need my insurer to get involved to pay for the repairs and then fight for the claim. Luckily for me has been straight forward.
Spoke to my dealer and the third part insurer who all said similar to the above.
For me, if there is a next time, I would prob go via my insurance company, but I am too far down the road as the cheque is coming next week and the caravan is now booked in. Plus, based on the calls, I am confident all will be sorted.