find a dentist/practice you like and trust, and go from there. Fees for treatment on the NHS are set. The initial examination/cleaning if 17 pounds. My husband had a filling and it was an additional 40 pounds.
We lost our NHS dentist here and had to find another practice, which we did. It's small and very personal, but most importantly, we like the dentist. We checked on private pay costs and they were more than double.
If you aren't with a practice, a private dentist will charge for initial exam, cleaning, evaluation and THEN the actual procedure, just like in the US. It may be cheaper than you were accustomed to, but may not. Just ask.