My little boy was hit by car but I didn't get the number plate, how can I claim medical expenses?

My little boy was hit by a car while crossing the road, he is only nealry 3 years old. I did not manage to get the number plate. My little boy has spent time in hospital and has been left with having fits for how long.. myself nor the doctors can say.

How will I go around claiming and would my son even be entitled to anything?