Car reversed into me in car park (England) and now they wont supply insurance details. Next steps?

I was driving in a car park and a car was reversing out of a space and hit my drivers side door. They were apologetic at the time and there was minimal damage to their car. A witness said that the reversing car didnt look and I wasnt at fault (but i stupidly didnt get the witnesses details!).

Contacted the driver today and she has said i was driving too fast and she couldnt react in time. I personally think she hadnt even looked at all. Car bodywork repairer has quoted £1900 for a full car door (its a new car so he did not recommend to do a cheap repair). She doesnt want to go through insurance because she is young and it will affect her insurance - but equally says she cant afford £1900.

Ive left the ball in her court and am waiting for her to reply with her insurance details but have been waiting 12 hours now.

If, theoretically, she doesnt respond with details - what do I do next? Thanks in advance

Edit: Thanks so much for all of your help. This is my first and hopefully last incident in 13 years of driving, so I was pretty clueless. Will contact my insurance. Thanks again. Reddit is great :)