It's not about this
Really glad you're ok and very sorry to see the state of the Mini.
A similar accident happened to me about 15 years ago in a 2 month old Audi A3. I was concerned about the condition of the car after such a significant impact and questioned the decision by the insurance company to repair the vehicle. As a compromise, we agreed that An independent AA inspection be carried out. They found that the chassis had twisted and advised that the car should be scrapped. You may wish to consider a similar approach, at least you then have some peace of mind on the condition of the Mini.
Most insurance companies offer a new replacement if a car is less than 12 months old and written off. My understanding is that Gap Insurance only comes into force at the start of the second year. You can also buy Gap Insurance for several months after the purchase of the car, try a google search and see what is available. Also, it maybe a good idea to ring your insurance and check the terms of your cover.I totally agree about the insurer's own repairers, which is why I am having this done by my local mini dealer. if the chassis or similar is significantly damaged they will add it to the quote. I didn't opt for gap insurance, so if it is written off, I'll have a shortfall to pay