Getting a non-emergency appointment at all even at our local private dentist was a nightmare for ages post-covid. They were taking none at all obviously taking no appointments during the lockdown-era, but then they had a massive backlog of people wanting appointments so if you tried to make one it was like "Uhhh how about half 2 on Wednesday... in June next year?"
This thread has just reminded me I need to book with the optician though
. Takes ages to get an appointment there too.