Given the third party fled the scene, which is a criminal offence and the police are satisfied you were not at fault (backed up with CCTV evidence), the third party would find it very difficult to dispute especially in a court.
I’m not sure whether Motabily insurance with Direct Line has legal cover included or you have cover elsewhere, but I’d certainly ask Direct Line if its included so you can pass on the crime reference number and CCTV evidence and let a solicitor deal with it.
Remember you have evidence, don’t be pushed into admiting liability by Direct Line