It depends upon the offer. If you are not happy with it, open a dialogue with the insurer. Have a look at comparable vehicles that are for sale locally and print them out, pull together any evidence of servicing, recent work done to the car, etc., and show the insurer.
At the end of the day, the point of insurance is to be put back in the position you were in before the accident. You have an even stronger moral case to put to the insurer if the accident was not your fault.
The only car I claimed as a total loss was stolen, and my insurer at the time (General Accident) made a very fair first offer indeed, and I accepted it. They did warn that any reassessed offer may not necessarily be higher.