FWIW, I did take the first offer when I was taken roughly from behind. I don't think the driver's insurance company even knew the extent of my (admittedly not very serious) injuries. I expect they were just scared by the amount of claret. Anyhoo, my insurers said, tjhey've offered £x, standard scale for cut head, concussion and night in hospital is £y. My financial losses were £z. Adding y and z together suggested that the £x offered was generous/over the top, s owe went for it. Reduces the drawn out nature of the whole thing and helped me put it behind me.