Incident on private car park

Whilst attending the Lincolnshire showground a few months ago with a work colleague working at the showground I parked my car in the private car park for workers at the showground, not accessible to members of the public. It was very windy and I got out of my car and went to the rear of it when my colleague got out they were not holding the door and the wind blew it open hitting a parked car next to them. My car was not damaged but there was a small dent in the other car.
We left our details and they got a quote to repair their vehicle which was very high but would not go to another garage to get a comparable quote. My colleague who had negligently let the door go doesn't want anything to do with it and my firm initially said they would sort it but now I have received a letter from a solicitor who have got my details from DVLA.
I feel I am now in a position being held responsible for something I haven't done or had any control over.
My thoughts on this are;
This was a totally private car park not accessible to the public and so not a public place under the Road TrFfic Act

Whilst this was my vehicle I think any actions bought by the solicitor should be to the person responsible and negligent for the damage, a civil claim against that person as I was not even in the vehicle.

Has anyone have any thoughts or professional knowledge if my assumptions are correct in law, or am I barking up the wrong tree?