imho I would never pass my insurance details on unless it was going to court, if it ever got to that stage by then you would have consulted a solicitor anyway and they would advise when the time is right to cooperate and give the other side the information.
if your confident you have done the job right collect all information that is relevant photos/paperwork/witnesses (did you have anyone helping you at the time etc) get it organised and have a free solicitor consultation.
Do not agree to anything, talk to the other side, communicate in any way what's so ever unless you have sought good legal advice. Others may disagree but you can stitch yourself up by just handing over your insurance details in the belief that the insurance company will protect your interests, they won't and may settle due to various reasons, which will affect your insurance in the future
It happened to me a few years back, glad to say not my fault but bent over backwards in time and money and then when all done, they got in touch with their insurers..... Ignored everything they chucked at me, spoke to a solicitor, was within my rights. I was happy to go to court, never happened. I was insured but I did not give my details as that would have opened a can of worms.
sorry for long post, in a nutshell don't do anything until you've spoken to a specialist solicitor. Good luck mate