Let's assume that you value the car at £10k and not a grossly owner inflated amount. You will probably need to argue the toss with ins co who may initially offer (say) £8.5-9k

From an ins co perspective if they authorise repairs of £6.5k they will then need to provide you with a hire car for several weeks even assuming required parts are available. It is also usually the case that a cat D car will reduce the vehicle value by 10 - 20%. In summary the insuarance company will pay £6.5k repairs + (say) £1.5k cat D depreciation + (say) £1000 car rental. Total about £9k.

The alternative is they write off the car and pay you £9-10k. They sell the car through the trade (who may use pattern and s/h parts etc) as cat D salvage for around £3k. This is probably less than authorising repairs themselves and means that they are able to simplify their work and close the files within a few weeks. No risks if repairs not done properly, extended repair times, no comeback etc.

They may be open to a negotiation if you feel strongly about it - personally I would do my best to negotiate o good settlement and take the cash.

My car was damaged a year ago; the third party immediately admitted blame so their insurer assessed the damage and offered to write my car off (it was 9 years old). They trawled the market and offered £3500, a reasonable stab at what it would cost me to replace it like for like.

As the car was structurally unimpaired I decided on a local bodywork repair. The insurers agreed and offered 35% less, which was just a little under the cost of my repair. So at a small cost I got to keep a very reliable car. It's probably not worth much now, but it's still running.