Has to report it to insurance asap. Some insurance writes in black and white that you should never admit your fault without informing Insurance. Of course in your case, you didn't, I supposed.
Police will eventually issue a report confirming who's fault was it but takes very long time. In the meantime, if you claim insurance, you have to pay deductible first. Your insurance will liaise with the other party's insurance to claim the loss amount. this could take long time as in most cases. With the police report issued to you, you can then send to insurance company and through them, you could claim your deductible from the other party's insurance.
There's another way to settle it is if that party agree to pay you an amount and you accept it. As he may not want to claim his own insurance as well.