Firstly, do you have knowledge of how much it cost to repair a car? It is very often I hear this comment, when the person making it has no knowledge. When you damage someone elses vehicle, you are ultimately on the backfoot. You cannot insist on where the vehicle is repaired or how. Without knowing how hard you hit the other vehicle, but assuming it was a minor parking manoeuvre, there is no way you will have caused structural damage. But if you have marked the bumper enough to cause distortion and broken the paint, the whole bumper will need to be painted. The paint and materials cost alone is approximately £120, then the labour to remove and refit and paint the bumper is around si hours. Retail rate would be approximately £50 per hour, £300 labour, with paint and vat = £504. That is how easily cost mount up. Dependent on where you hit it, it may require blending to a wing, so it would increase again. £750 is over and above what I would expect based on the limited information. Request a full copy of what work has been estimated. Your excess only relates to claims for damage to your own vehicle not theirs and ultimately your no claims will be affected if you do not pay for it yourself. You can advise your insurer you feel that the third parties quote contains "unrelated or unnessary" repairs and request they inspect.