Inefficencies exist everywhere!

My car was involved in an accident by another person, who accepted complete culpability, when he entered from a side street, and I was stationary. Not much damage was done except that it is now not roadworthy as the turn indicator light is damaged. The required three quotations were supp**** immediately to the insurance company, who then decided to do nothing. After two months of battling to get a decision, finally we were offered to receive a cash payment in lieu of the repair bill. well, after two months the quotations were out of validity, and I requested that a revised quotation be accepted. TO NO AVAIL. I must simply accept the cash originally offered. Who now is responsible for the balance to pay, as the new quoation is slightly more than the original?