In this situation the address doesn't really matter. I know people who have been in the same situation and it wasn't an issue, the vehicle was even collected from a different address to the one declared on the insurance.
What will happen is the designated repair place will recover the car, assess the damage and fix/write off accordingly and deliver it back or allow you to collect it.
If the car was stolen or vandalised, police would no doubt be involved and if it was clearly stolen from an address the vehicle has been stored at for some time you'll run into big problems.
I am no way condoning lying about the address however if you should go through insurance it probably won't matter in this instance. No claims will be adjusted if they deem it your fault though (it was).
Thanks for that sensible answer. I am going to see what the other party wants to do first as she says she's getting a quote from a body repair shop today and will contact me later on or tommorow. IF she wants to go through with body repair work does that mean she would expect me to pay for the damage or would she out of her own pocket?