Have you contacted your supervisor? They may be able to help add a bit of pressure. You shouldn't be left in this position, especially running up bank charges.
My university was very experienced with handling research council fees, including AHRC who funded me. But I still had a mix-up, where I tried to matriculate one year, and there was a debt marked on my account because my previous batch of fees had apparently not been paid. Oh yes they had, I checked when and everything with the funding council. But I still couldn't matriculate, until Registry put me through manually. Thank goodness that was in my final year, so I didn't have to go through it again :)