In a shock move, dealing with my insurance company was surprisingly straightforward, and everything got sorted pretty quickly.
Probably because everyone figured out pretty quickly that it definitely wasn't my fault, and the other driver's insurance company would be liable.
The worst part was spending about an hour on the phone with the insurers, where some call-centre agent basically read me all the contract details for getting my car repaired, and getting a courtesy car, and getting an insurance policy to protect me if the other insurer didn't pay up and the repair bill ended up coming back to me (which, despite being an insurance policy, is something I didn't have to pay for).
It seems like this is something they do all day, so not only are they completely familiar with the terminology, but when they read it off their screen all the words blur together, which makes everything doubly hard to understand. Also, when they've been explaining about repairs, and courtesy cars, and then rattle off some "small print" referring to "the service", it's not always clear which service they're talking about when. But when you ask them to slow down and go back a paragraph, sotheyaren'ttalkinglikethisanymore, they... start... talking... like... this... instead.
The weird part is when they go over something that seems pointless. Like "if you cancel the service within 15 days, you will then be charged for it and we won't cover it." "Uh, why might I do that? I mean, why would anyone cancel the service?" "I don't know. I can't think of any reason." "Why are you telling me this then?" "It's just something we have to make you aware of. Don't worry about it."
Surely, if you have to make me aware of something, then that means I have to understand it. If I didn't have to understand it, why bother? But in that case, why tell me things that don't make any sense?
Never mind. After all that, the next day I went to the mechanics they asked me to go to to get the damage assessed, and a guy just took some photos of the superficial damage to the body panels, noted down my mileage and a couple of other bits, and told me it would probably be uneconomical to repair. And that was that.
A couple of days later the insurance company got back to me, told me they'd determined that the car was uneconomical to repair, and they'd pay me the full value of the car in lieu of repairing it (~£750) but let me keep it.
So I took it to a mechanic near where I work and got them to actually check for mechanical damage. Even though I'd been driving it around for about a week at this point, and couldn't feel it pulling to one side or any strange vibrations, I had noticed that the wheel that had been struck wasn't entirely true anymore, and had no way of knowing whether anything was at all likely to suddenly snap or fall off.
Turns out everything was structurally sound. I just needed the wheel arch knocking out a bit to ensure it wouldn't rub against the wheel if I hit a vicious pothole, and the bumper riveting in place to make certain it wouldn't start flapping about at high speed, and a bit of (mismatched) undercoat on the bare metal to protect it from the elements. And a new rear numberplate light. That, plus a new MOT for the insurance company to let me keep my existing policy until it's original end, came to ~£150, all in.
So I made ~£600 on being hit, and now my car has authentic battle damage!