It depends if you have independent witnesses.
If not, it is the other driver's word against yours, and if you are hard-faced enough, you can claim he reversed into you if you wish to go down that path.
If you are looking for the moral response, then ask the drive to obtain two quotes for damage repair, and weigh that against the loss of your No-Claims bonus if you proceed through your Insurance Comapny.
If the cost is less that your Excess and NCB, then settle personally - if not, claim through your insurance.
You have two options the hard-faced way, and the way i suspect you will wish to go, which is the morally correct way - and that is the second and simpler option.
The first simply involves toughing it out and lying until the other party gives up. It's not what i would do, but plenty will. The prersent Mrs Hughes is enbroiled in a damage dispute where the driver was uninsured, and is telling his Insurance Comapny that his wife was drving! Without independent witnesses, he may get away with it.