Not a great deal of help to the OP, but I had a similar thing a month or so ago (Guy reversed into me, as I was waiting at a Carpark exit). More off a glancing scuff to the off side front bumper. I took it to a local body shop and it was going to cost around £200 for a mobile repair (auto restore, Chios away etc..) or a full on non insurance quite was £450.
I explained the the guy who hit me that I wanted a ‘proper repair’ at £450. He baulked a little but agreed, from then on, No issues in getting it sorted or him paying, worse bit I guess wad I had no car for 2 days.
Hope you get it sorted however it pans out