It is really ridiculous when you think about it. You pay for car insurance so that if anything happens to your car, you are protected but you cannot even make a claim under these circumstances because your premiums will go up when it's time to renew. How much damage has been done to your car? Have you taken it to a garage to get a repair quote?
If the costs to get your car repaired amount to a lot, then you can get hold of a hit and run lawyer but I doubt you'll need that since you said you don't want to claim on your insurance, so I'm assuming you'll be taking it on you to save you from any hassle. The CCTV is operated by the council if it's on public road, so you can contact the local council where that happened and ask if you can get the CCTV footage. Let me know that you were involved in a hit and run and that it's not fair that you should fork out the money to pay for damages to your car when you were not at fault.