Has anyone bought back their insurance write-off?

[Reallybadidea]

Has anyone done this? How did it work with getting insurance and selling it on in future?

Looks like our car is going to be written off after hitting a deer, which has caused damage to the front bodywork, but we don't believe there's any problems with the rest of the car and its otherwise in good condition and reliable. I also don't want to be without a car while we find another!

Yes. It was a fair while ago so things may have changed. The transaction was with my insurers who simply deducted the scrap value from the settlement figure and I kept the car.
In my case it was relatively superficial damage on an old low value but relatively rare model. I had rear lights and trim replaced using SH parts and also got a fresh MoT. Your insurance will expire on the payout so you will need to reinsure it. It will carry a marker, Cat D etc, giving the category of the right off and this will impact on any future value. In my case I ran it for a couple of years and then sold it to be stripped for parts.

If it has had a heavy impact I would get it checked for example twisting for safety.