there is no standard charge for private dentistry it is upto the dentist for companies to standardise charges is called price fixing and is illegal and can lead to heavy fines as many organisations suh as airlines etc have found out
whether NHS or private you should have a treatment plan and estimate, however when someone is in pain the prioroty is treating pain and so there is aimplied consent... my back tooth is hurting... it has a big hole .... can you fix it.... yes we can....... today? yes i'll do it now.... that is consent
yuo should have been told cost though as extraction may have been cheaper option not that i would advise an extraction
I would say in UK that 500-600 was about right for a complete root treatment on a molar/back tooth inlcuding re filling but not if it needs crown. according to latest figures that is about average charge, but that is for completed root filling not an emergency get you out of pain appointment as root fillings often take 2or more hours
NHS charges in England are in bands. in scotland still previous system where each item cost a certain fee , on maternity leave now but root filling s on back teeth were approx £100-150 with all xrays and new filling on top 3 years ago
But I agree there is a considerable breakdown in communication about finance and other things so OP does have grounds for complaining, write to practice first, you can take it further later if response inadequate but keep it polite and factual ; you obviously knew it was not NHS as you were on denplan before and denplan tends to lapse if you do not attend regularly
Good luck and hope toothache gone