The TP ( or his/her insurer) is legally obligged to put you back in the same situation you were in prior to the crash.

That said as they have offered you the book value then that seems fair.

If you reject this then the onus is on you to prove that the value of your car is more than this. You then claim this amount as the repair cost .

You will have to justify why your KA is worth £800. Not just your wish for whatever reason but justification. You will need to justify this through the courts as the Insurance company will no doubt claim they have treated you fairly.

If you win then you get your car repaired, if you lose then you get more costs and end up poorer with no car.

I would take the money and run

you can come to an arrangement with them whereby you receive their offer and keep the car, its unlikely to be enough to repair the car i feel.....if you wish to kkep the car on the road for sentimental attachment then more power to you,but insurance is brutal,plus the car once repaired will be registered as as accident damaged and then that affects future insurance!! you cant win!!