When a vehicle is written off it just means it's "beyond economic repair". That's if taken to a garage for repair. If the damage is light, anyone can but the car and repair it. A DIY repair cost a lot less than a garage repair and can make economic sense. Depending on the severity of the damage it may need a government inspector to check the repairs.
To find out if your vehicle is still on the road, goto
https://www.taxdisc.d.../intro?skin=directgov and click on "Vehicle Enquiry".