If she's "fully comp" then they must pay out. Under the Road Traffic Act 1991, as long as the vehicle is insured then the insurer is liable for your loss. It's mandatory that cover is provided for third party risk. Was the other party's vehicle stolen? Enquire with the police. If it was, the at fault insurer cannot deny the claim. If it was not stolen, the owner is still liable as they must have control of the vehicle at all times (i.e. know of who is using it with their consent). The car has either been stolen, or they have been negligent. The at fault insurer may try to argue that unless the driver can be identified they are not liable, but they are always liable. Have a good read of the Road Traffic Act relating to insurance. If the vehicle was not insured, or the driver cannot be identified, then your sister-in-law can claim through the MIB: www.mib.org.uk/

One Call needs to do what your sister-in-law has paid them to do, indemnify her for her loss and pursue this loss on her behalf.