[WhiteTiger]

Since you have their info, but they are runners, this'll require a unit dispatched to you for investigation (don't bother going to a district office, they'll tell you as much and send you on your way). Call up the non-emerg line and let them know what happened and that you have the other vehicle's information. They'll set you up a call to have a unit dispatched to your place.

During the officers visit, be sure to ask at some point for the case number (You can even ask the ECO answering the non-emerg line, at the end of the call if you like). It's an 8 digit number, and will start with 20xxxxxx. That's what your insurance company is looking for.

Your insurance company is perfectly capable of getting a copy of that report from the police themselves. I only mention this as they occasionally seem to tell their clients (you) that you have to get a copy and send it to them. So far as I know, they do this to be cheap. As a person involved in the report, if you go down to a district office, you can get a copy for free. IIRC, insurance companies are charged per copy. If you want to get a copy and mail/fax/email it to them, that's cool, but every insurance company is perfectly capable of getting their own copy.

ETA: The only place this gets a bit sticky is if the vehicle that hit yours is stolen or has been reported stolen. Then, to the best of my knowledge, you are out the deductible, but insurance covers the rest.