I need urgent advice regarding dentists / dental treatment please.

My Nana has been having toothache for the last couple of weeks. She's taken paracetamol for it and we managed to get an appointment with her dentist earlier this week. When she called them the first time, they said they couldn't give her an appointment until late, the day after. She said she was in a lot of pain so the receptionist gave her an emergency number to call. When she called the number the answering machine message indicated that they were unavailable/closed. Calling the dental surgery again she went ahead and made the appointment for the next day as it was better than nothing.
The dentist was nice enough, took an x-ray and told her that she has an abscess in her gums around one of her molars. She gave Nana antibiotics for it but said that she will need to have some kind of root canal treatment. Her gums need treatment as well (apparently due to one of the medicines she's taking for a pre-existing condition) and the tooth might not be able to be saved.
Apparently the machine that will be used to treat/clean it will be better or dentist will be more thorough if we do it privately. She said that even if she does it privately it doesn't mean that the tooth will definitely be saved, although the chances of losing it will definitely be lower.
She quoted various costs very quickly so from what I gather, although Nana could have the treatment done free on the NHS (she's 80 years old), dentist made us feel like it would be a more thorough, better job if we did it privately. We definitely got the sense that she was pushing us in that direction by even saying that if it was her own Nana she would do it privately.
Also, she said that there are different....fillings?/implants? that would be needed afterwards....again, she quoted so many different prices up to £1400 for the varying qualities so overall cost would be nearly £2,500. It was a lot of information to take in and although I asked for any literature with details of what the treatment entailed and pricing she said she didn't have any to hand and we should simply call her after completing the antibiotics course to let her know whether we want to go private or not.
Thinking about it now, I'm not even sure I trust the dentist to do a good job since it came across like the money was more important than Nana's tooth/teeth & wellbeing. Maybe I'm being paranoid? I don't know.

I know Nan is elderly but that doesn't mean we want her to have any substandard treatment, which is what the dentist made me feel it would be if we went the NHS/Free route.

I don't know what I'm expecting from you guys but I do remember reading about various FMUKers having problems with toothache/dentists.

Any advice about what to do in this situation, or even advice about whether one can just go to the hospital to see emergency dentists would be helpful?
Please, any advice on this matter would be so helpful and I would be so grateful because I'm currently at a loss as to what the best route would be and even if the options we have been offered are any good.
Thanks for reading.

P.S. Please excuse my grammatical/otherwise errors. I just typed that in one breath(so to speak) as I'm upset because Nana is in a lot of pain and paracetamol isn't helping her enough.