It depends on the insurance company if you can buy it back. Some have contracts with underwriters who buy all the write offs from the company, some dont.
If you dont make a claim the car is yours to keep, so you need to weigh up the price differences yourself. Total in the fact your insurance premium will go up after the claim as well, it might be finacially better to buy a good shell and swap over all your parts rather than claim the money for your car, lose all the parts and start to rebuild another. Thats what I did with mine and you can make a bit of money with any left over parts and sell whats left for scrap.
I would see what they are offering for your car, remember its YOUR car to decide to do with as you wish. If they start telling you you cant buy it back and have to scrap the car tell them its your decision wether or not the car is repaired to satisfactory standards to keep it road worthy and they can take their shitty settlement payment and shove it back up their arses where it belongs.
They are in the business of making money for themselves, they dont care about how you feel about your car. They will probably offer about £300 over the book price as it has a few mods on it, and some bastard will make a killing selling off the parts.