After initially needing

After initially needing a filling for a small cavity, I had to go back to my dentist three further times in the next 2 months; to get it refilled due to it being too high, extreme sensitivity, and a fracture on the front face of the tooth. I’ve now been told I need root canal due to an infection under said filling, which I am being referred from my NHS dentist to a private practice who have quoted me £695! I believe this is not my fault and that bar the need for the initial filling, all subsequent treatments have been required due to the dentists error.
My question is how can they expect me to pay this private fee when my NHS dentist has caused the problem. Is there any one I can complain to about the situation, and why am I not able to have the treatment on the NHS at a much reduced cost?? Thanks in advance