its difficult without specifics, and i'm only familiar with US insurance, specifically FL, but in general ...
its quite normal for your company to pay you (minus deductible) then subrogate against the other carrier and recapture the ded for you., not sure if its mandated that way, usually when the other company gives a lowball, customers go to their own company for a better offer, find out if you can do the same, ie: call the other company and see if they will settle direct, and bypass your own company.
use and collect as much data as you can on comparable cars... in addition to nada, kbb, and auto trader are used frequently by companies in the US, think of it as a "job" since if you spend 2 hours collecting data, and it makes you $500 more, then your making $250 an hour, so DON'T be lazy about it, take the time, (not 10 minutes) to collect the data to plead your case. you want a detailed list of cars IN YOUR AREA with price, mileage, condition, photo's, as many details as possible... for example if you see a comparable truck with more milage, but signifcantly less expensive that your estimated replacement, then make detailed notes about it, and why its not comparable, use any and all excuses as to why its not comparable. if a comparable is NOT in your area, get a shipping estimate, (get a high one) or two so you can say "this one might be comparable, but it will cost $900 to ship"
I repeat... 10 minutes of research isn't enough... if you want to approach it with 10 minutes of work behind you, you will lose.
collect service records, what's been done recently, new tires, brakes, shocks, stereo, whatever you can think of.
rack up the rental usage in the meantime, spend as much as you are allowed, it will encourage them to settle faster (that helped me recently, since I knew I could drag my feet over an offer, and it was costing them $300 a week for me to do so)
be polite, but firm, ask for their comparables,, you want to see which specific vehicles they are using to make the comparables, then you can look up those vehicles yourself and find out if they truly are comparable. don't just accept a number, you wan to see how they came up with that number.
now... whats funny, my daughter had a total in a not at fault, and I did all that work, expecting to go to war, and the company offered my $700 more than I was planning on fighting for... and I was shocked, I still sat on it for 2 days , then called and countered with, i'll accept it if you give me an extra week on the rental to shop for a replacement, they said OK