When should I tell my insurance company about the accident?

As soon as possible. Your insurance policy may have a time limit for reporting accidents. If you miss this deadline, the insurance company will deny your claim. Just as in your conversation with police, when you talk to your insurance company, stick to the facts. If you are pressured to “take the blame” or to blame someone else, simply say that you want to see what the results of the investigation are before you say anything else.