Its your choce wether you go through the insurance company or not. Thats what you pay insurance for. They are responsible so u wont loose your no claims.
I would get in touch with your insurers and pass on the details of the car that hit you. They should do the rest.
If theyre bein sh!tty about contacting theire insurers its not your problem and theres more of a reason to get their insurance involved, just to piss them off some more! What ever happens, make sure you dont do badly out of it! Its not your fault!
Could be worse, it could have been hit by a train...