If your car is written off, you should not be stranded
A write-off decision isn't the end of the process. It's the start of a conversation about what the car was worth, and those take a while.
The practical problem is the gap in the middle. Your car's gone, the money hasn't arrived, and you've still got to get to work on Monday.
On a properly handled non-fault claim you can usually keep the replacement for up to seven days after the settlement cheque lands. That's deliberate. It gives you room to find the right car rather than taking the first thing you can get.
If the valuation looks low to you, say so early and put your reasons in writing. Advertised examples of the same car, same age, same mileage are the most useful thing you can point at.