In 1999, just

In 1999, just after I finished University, I had NHS root canal treatment in a canine tooth at a dentists near Leeds. The dentist did not inform me of any of the risks of this procedure. Following the procedure my tooth died and went black. What came to light during an x-ray check-up in February was that the dentist had broken the bit of the drill in the tooth and not told me about it. but what I only discovered in February. Now my dentist (in Loughborough where I now live) has told me that it is infected due to the presence of the drill bit and the infection has spread to the bone. I have been told that I have to have private secondary root canal treatment which he says I can’t get on the NHS. This will cost me £69 for an assessment and then a minimum of £540 pounds if they can do it simply, otherwise it will be much more than this.
I don’t have this kind of money, and it seems very unfair that I have to pay for this, is there anything I can do get compensation to pay for this corrective work from the original work? Thanks very much for your help.