Not sure what more you can do aside from keep on at the finance company as it is them that you have the agreement with, not the supplying dealer. Have you spoken to them on the phone and confirmed that you are sending the letters to the right place? If you do end up having to tax it in the interim, you can reclaim any unspent full months of the tax disc at the post office so not being too out of pocket.
I would call the finance house and speak to a manager or somebody higher up than a call centre monkey and ask for a name who you can address a letter to personally.
Sounds silly, but you don't live anywhere near the finance company's address do you??
JJ