Don't let the car be towed away, you will have less chance of getting it back!
if it is written off it will be recorded as cat d possibly c but i doubt it.
once written off the insurance co then pay you out an agreed value, the car then becomes their property, you then need to ask to buy the salvage from them.
They will usually sell on to a salvage company , hence why salvage companies exist.
I would personally communicate through your company at first, thats what you pay your premium for, their services!
Whats that old saying…. 'The best person to buy your car is an insurance company!'
If you feel their valuation is too low, collect any paperwork you have for recent expenditure and any evidence of similar cars for sale.
At the end of the day it's not your fault, why should you suffer any loss