[timon]

There's only one thing you can do: give them a hand at determining the current replacement value for your car. As repairs will outweigh the replacement value of the car, it is going to be a write off in the end. You have to find the most expensive cars for sale, similar to yours (specs, body condition, mileage), add their price to a list and ask the insurer to fix the replacement price at the average price of these cars. Send them the list as proof.

Obviously your own insurer isn't willing to make any expenses as they don't even want to send a surveyor for physical inspection. Maybe cut them off and communicate directly with the third party's insurer and kindly force them to send someone for inspection. Tell them it's a joke to think it's possible to determine value on the basis of photos: one cannot see the difference between a cleaned up pile of junk and a decent car from distance.

Don't trust your own insurer, it's very unlikely they'll question anything the third party's insurer asserts.



Edit:
If your car underwent any (big) repairs, tell them to take that into account as well.