As it is a new 'van, ask your dealer to throw in the adapter and the pin alignment 'tool'. You can get them both for under a tenner, so hardly a deal breaker for the dealer.
We had to hire a Discovery to tow our new 'van on it's first holiday. We bought a 13 to 7n 7s adapter, used a cable tie to attach the adapter to the stabiliser handle to secure it out of the way. 700 miles of towing, no issues.
Once you have the adapter you can keep it in case you change your car for another with 7n & 7s again, or someone else tows your van for you.
Depending on your car, you don't say what it is, it could be pricey to change to 13 pin.
The pin alignment tool is something you get with the 'van imo. A £1.25 retail item should be in the pack you get with the 'van. We were advised that the 13 pin 'van plugs often move alignment this tool saves lots of hassle. And yes it does happen as we found at Xmas when trying to leave site for home.