A month has passed and I still haven't had my claim paid out

I was in an accident a month ago and I have yet to be paid out for it. At first it seemed like things were moving in the right direction. I sent them the documents they requested, I gave them the spare key etc etc. And then I heard nothing for a week. I tried calling, sending emails, the whole lot. Eventually After sending emails to people who aren't even involved in my claim I managed to get the person handling my claim to respond to me. I asked them whether they could tell me how long it will take for the money to be paid out to me, which was met with silence. My claim has also been passed around like a game of hot potato between at least 5 different people now. People are either out of the office, on leave, not going to deal with my claim, or just plain ***********.

I am in the process of buying a new car, but I can't actually buy it without my claim being paid out. The seller is becoming increasingly frustrated with me because of this, which is understandable. I am very unhappy about the way this is being handled.