Reg plate and sound was caught on dashcam, actual point of impact was not.
I believe I can prove from the footage the registration of the car that did it, but there is a doubt the other insurance company will launch a CSI style investigation to prove me wrong. Since no one was injured, I doubt the CPS will prosecute in the criminal courts because "It's not in the public interest"
If I want to take it to the courts myself I believe I would have to pay fees (even though our taxes pay for this!)
I have Comprehensive cover (not sure if this is applicable as I am not making the claim) I also have legal cover (would I be able to use this to cover costs in pursuing the insurer?)
The audio is probably not enough for a prosecution, but CPS/police do not prosecute people for accidents because accidents are not illegal, only thing they could go for is not reporting it to you or the police within 24 hours, and unless someone was injured or the damage is very serious, that is highly unlikely to happen.
You could go to their insurer and if not successful use the small claims court and probably win easily at no cost because they wouldn't turn up to defend themselves, it would not be worth their cost of turning up to avoid your claim. You would still need to inform your insurer of the claim though, otherwise your insurance would become invalid, and of course the other insurer would put you on the list of people who have made claims, so your insurer would find out if they checked because you make another claim or a claim is made against you.
Your legal cover probably does cover the costs of chasing the claim, but you would normally use that by going through your insurer, let them deal with it, and the legal cover would pay any costs. Sounds like they wouldn't have to fight the case anyway, but having legal cover will make it easier to convince your insurer to fight it rather than settle for 50/50, without the legal cover I think it is their choice not to bother, with legal cover I think it is probably your choice, I'm not sure on that bit
I believe I can prove from the footage the registration of the car that did it,
The plate does need to be clear, but presumably the police have already confirmed it if they have given you the owner's insurance details?
I have Comprehensive cover (not sure if this is applicable as I am not making the claim)
How much damage is there?
I think you are making a claim. If you have a decent insurance broker then you should be able to ask their advice, including about using the legal cover you bought through them, remember that most UK insurance is not bought direct from the insurer even if it appears that way.