If you suddenly have a dental emergency and have to go to an out of hour’s dental clinic, you should be able to find one in your local area if a city or somewhere in the town. These are usually private companies that are part run by the NHS and you will generally just pay a prescription charge and a check up and treatment fee of about £20 (not London). If you are working full time, you might not be eligible for NHS treatment and they may charge you a lot more than £20, and you won’t always be guaranteed to get treatment if they have assessed you over the phone and determined that your problem is not severe enough to count as an emergency; you usually can’t walk in and expect treatment as they usually assess over the phone and you are more likely to get turned away. It’s only a good option if you can’t actually talk over the phone and have to write something down for them as you answer their questions that way; don’t expect any sympathy from them though if you try to get there-and-then treatment using that approach.
Usually if you fell over and chipped your tooth and there is some blood they won’t offer you treatment, same if you have toothache and there are no loose teeth; they usually tell you too book an appointment with your regular dentist and wait for that appointment.
Once you get an appointment with them, they expect you to arrive 15 minutes before your appointment to fill in the paperwork they need, but your appointment could be any-time from 10 minutes to an hour and a half after your appointment time depending on when you go there and availability of their staff. It’s quite common for them to ignore patients when they are short staffed and have to take a break; just be glad there is a service that can help you and don’t create a scene if you do end up waiting more than an hour.