Yeah its a pity you didn't give the driver a cup a tea and say
" and who is er your insurer ? "
If your insurer is paying then they will recover from the car drivers insurance by a thingy called subrogation
see
http://en.wikipedia.org/wiki/Subrogation
This can turn into a horrific run-around - and the police should not have told you to contact your builders insurance - you could for example have sued the driver direct. Hence the cup of tea bit....
In my own case the employed driver gave me the address of his employer and we were officially told the firm was uninsured, so I started proceedings direct and the employer said I don't know why you are doing this I am insured....
and then my own insurance said hey ho your own car insurance in dicky so we are repudiating your insurance and I said - but that doesn't matter because the other guy had admitted liability, and they said ........
anyway good luck