Don't understand what the issue is here.
If you're not claiming - how come they got to see the quote for repair and decide to write it off ... ? It wasn't an accident for the purposes of the road traffic act - "If owing to the presence of another motor vehicle an accident occurs .... " so there was no need for any issues to be raised with the insurer at the outset. Now that they know - they will write it off as the repair is more than the value of the car.
If I were you - let them write it off - buy it back and punt around in it with a few quid in your pocket. The damage as far as I see it in terms of the insurance company - has now been done.
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