They will write it off, negotiate the salvage value of the car and deduct it from the payout. You will be able to fit good second hand parts to get it back on the road and be in pocket too. Never take the first or second offers of value but they rarely up the offer after offer 3.
Don't forget to tell them about any recent serving or expenses paid out recently. You can if necessary put your number plate on retention online and it is done immediately.
Not sure if this is what you mean but... if you are saying let the insurance company write it off then I can't agree if there is another route available. A repaired Cat will never be worth more than about 60% of it's prior value.
I have a serious issue with the whole Cat thing mainly on older cars but on newer ones too. The insurance companies have it all their own way to manipulate the situation to their advantage. They know exactly what cars fetch at salvage auction and will manipulate their decision based on this. They will happily write-off an economically repairable car if they can improve their financial position from the salvage - regardless of what the repairs will cost.
When you go down a claim route you are surrendering the future of the car into the hands of the insurance company for their own selfish gain. It's a good job house insurance doesn't work in the same way. They will even try and convince you to use their repairer if they don't write-off - rarely a sensible option as their repairers are usually national chains/networks, their work is often questionable anyway but even worse after being bullied into lower rates in exchange for regular work from the insurance company.
Let's say you paid £4k for the car and it had held at this value prior to the accident (no idea in this car's case but it conveniently illustrates my point). It's written off and there is a £4k payout - lucky btw if they agree with your valuation. The salvage is bought back for £1.5k - which is more than they would get at salvage auction btw as they take advantage of your emotional attachment. So £2.5k in the bag to pay for repairs. This needs to cover not only the repair costs but the drop in value after repair from £4k to £2.4k (40% drop to 60% of original value). So you have £900 left to do the repair.
With the right level of owner input and hard work, that car can I suspect be repaired for £500-£1000. But it will be hard work and a big learning exercise. And even if you can cover yourself financially then your pride and joy is forever branded as an outcast by most of society. It will be more difficult to sell even with the 40% price reduction.
Meanwhile the insurance company are out of the problem cheaply enough. Preferable even if they can get a repair done for less due to their overheads of processing a repair. They even get to load your insurance premium next year due to the claim. Protected NCB % is not the same as protected premium. Oh and they have your £400+ annual premium to offset their costs, not to mention the previous 15-20 years when you never made a claim. They are laughing every step of the way as they disappear into the sunset while you get to do all the running around to fix your car and have the issue of it selling it one day as a Cat. Or find a replacement in as nice a condition as yours.
I'd have a lot less problem if there was a separate category of write-off for older/cheaper cars that was never recorded onto the DVLA record. Or if there was a way to virginise a Cat N/D (potentially S/C) of the car by inspection.
Oh and add in this - if you decide to keep this totally away from the insurance company and settle with the party responsible then you are breaking the terms of your insurance by not notifying. And what constitutes an accident is anyone's guess. A low speed shunt into a gate post? A trolley rolling across the car park into your door?