Hit and run - reg plate noted

itn

hi, my wife had taken the car to work, she parked car on a side street, and somebody reversed into the car, looks like there was an argument on the road butwen 2 other drivers and on of them had to back down. My wife was at work and car was unattended. Somebody who was dropping off kids at the school saw this and noted the reg of the car who hit my car, she kindly informed my wife as she teachers her kids at school. I have reported this to police who just want me to fill in lots of forms, ive also informed my insurance company who adv i have to payy the access and they will claim it against there insurance company, they put the reg plate in there syste who told them who their insurance company was. My insurance elephant.co.uk said they will write to the cust and take it from there?..

anybody had a similer experience or can you advice further, will my claim against 3rd go through, what happends if they deny it?.. i have full details of witness which ive passed on?.