Firstly, you will need to tell your insurance company of the collision regardless of whether or not you are making a claim. If you neglect to inform them, then you risk voiding your insurance.
It’s also important to take into account the better service you will get going through your insurer. If you claim, you should get a full inspection of the vehicle with any damage taken care of. Sorting out repairs yourself with money from a third party might not address all of the problems. This could result in more serious issues down the line and an unnecessary headache for you.
Accepting cash from a third party in lieu of a claim might make sense for smaller collisions. Often, smaller, cosmetic damages are not worth claiming on when you take into account the no claims bonus you would lose plus the excess you need to pay.