your car is logged on a central database by the insurance industry once it is written off. The term written off is open to many meanings. Is the car uneconomic to repair or a total write off. In the former, you might be able to repair it and put it back on the road, in the latter, you cannot put it back on the road.
If putting it back on the road, you should have it comprehensively assessed by a qualified motor assessor. the reason being, that in the event of an accident, where you are at fault, your insurer may try to say that it was not in roadworthy or mechanically sound condition, thus putting you in breach of your policy terms and having to reimburse insurer for any payout made on your behalf.
In the event of another accident, you not being at fault, it will be difficult to put a value on the car. You cannot value it the same as a similar uncrashed model as per the 'salesmans guide'.